applied mathematics
Sistan and Baluchistan
Department of Mathematics
Department of Mathematics
Sistan and Baluchistan
BahonarKerman University
Ferdowsi University of Mashhad
Settlement and pore water pressure in soils during the consolidation process are of great concern for geotechnical and structural engineers. Therefore, different analytical and numerical methods have been proposed for its solution considering the complexity of soil behavior and geometry of soil layers. In this research study, consolidation equation has been solved using the matrix-based rationalized Haar wavelet transform method. Two typical and most commonly used cases are solved and compared with the classical solution method which is based on Taylor series expansion. The proposed method is fast, convenient and requires less computational effort due to its matrix calculation implementation and it yields accurate results when compared with the classical solution. Furthermore, this method may be used for implementing explicit functions rather than a constant value for the consolidation coefficient (cv).
Everyone knows about the complicated solution of the nonlinear Fredholm integrodifferential equation in general. Hence, often, authors attempt to obtain the approximate solution. In this paper, a numerical method for the solutions of the nonlinear Fredholm integro-differential equation (NFIDE) of the second kind in the complex plane is presented. In fact, by using the properties of Rationalized Haar (RH) wavelet, we try to give the solution of the problem. So far, as we know, no study has yet been attempted for solving the NFIDE in the complex plane. For this purpose, we introduce the continuous integral operator and real valued function. The Banach fixed point theorem guarantees that, under certain assumptions, the integral operator has a unique solution. Furthermore, we give an upper bound for the error analysis. An algorithm is presented to compute and illustrate the solutions for some numerical examples.
In this paper, the analytic solution of the absolute value equations (AVE) is investigated. As far as we know, there are some numerical methods to obtain the solution of the AVE. However, there is not a study on exact solution of the AVE. Here, we try to obtain the exact solution of the AVE based on a dynamical system model constructed by the projection function. Finally, the simulation results show the effectiveness and the accuracy of the method.
This work is based on using wavelet for calculating one-dimensional nonlinear Volterra-Hammerstein and mixed Volterra-Fredholm-Hammerstein integral equation of the second kind in a complex plane. So far, as we know, no study has yet been attempted for solving this integral equation in the complex plane. The main specificity of this method is to avoid solving any linear or algebra system for approximated of integral equations. In Section 2, we introduce the integral operator for RH wavelet and use it in our numerical methods. In Section 3, we show that our problems have a unique solution. Furthermore, we give an upper bound for the error analysis. Finally, we make some example in Section 4 and solve them.
In this paper, we introduce a new efficient numerical approach for solving of mixed 2D nonlinear Volterra- Fredholm integral equations. The fundamental structure of this method is based on the using of 2D Haar wavelets. Next, a detailed error analysis for the method is presented by applying the Banach fixed point theorem. This theorem guarantees that under certain assumptions, the analyzed equations would have a unique fixed point. Finally, some numerical examples are given to show the accuracy of the method, and results are compared with other numerical methods.
In this article, we propose new method to find a nondominated solution of a specific type of nonlinear fuzzy optimization problems, where all coefficients of the objective function and the constraints are triangular fuzzy numbers. For this purpose we use -cuts of the triangulare fuzzy numbers to convert the main problem to an interval nonlinear programming problem. The nondominated solution of the original problem by solving the interval programming problem is obtained. To illustrate the efficiency of the method, some examples have been solved.
In this work, we applied a new method for solving the linear weakly singular mixed Volterra–Fredholm integral equations. We now begin the theoretical study with acquirement of the variational form; in addition, we are using Bernstein spectral Galerkin method to be approximate to my problems. We estimate the error of the method by proved some theorems. Moreover, in the final section, we solved some numerical examples.
This study has been conducted to calculate the one-dimensional nonlinear Volterra–Fredholm and mixed Volterra–Fredholm integral equation of second kind in a complex plane, regarding the use of the wavelet. As far as we are aware, there have been no studies conducted so far to solve this kind of integral equation in the complex plane. The main feature of this method is that, it approximates the integral equations without solving any linear or algebra systems. In “Approximation of the Solutions with RH Functions” section, the integral operator for the RH wavelet and its use will be presented in our numerical methods. “Error Analysis” section, will discuss about the unique solution of the mentioned problems. Furthermore, an upper bound for the error analysis will be given. Finally, some problem examples and their solution will be proposed in “Numerical Examples” section.
In this paper we have introduced a computational method for a class of Darboux problem that change to two-dimensional nonlinear Volterra integral equations, based on the expansion of the solution as a series of Haar functions. Also, by using the Banach fixed point theorem, we get an upper bound for the error of our method. Since our examples in this article are selected from different references, so the numerical results obtained here can be compared with other numerical methods.
In this work, we present a method for numerical approximation of fixed point operator, particularly for the mixed Volterra–Fredholm integro-differential equations. The main tool for error analysis is the Banach fixed point theorem. The advantage of this method is that it does not use numerical integration, we use the properties of rationalized Haar wavelets for approximate of integral. The cost of our algorithm increases accuracy and reduces the calculation, considerably. Some examples are provided toillustrate its high accuracy and numerical results are compared with other methods in the other papers.
In this article, we present a method for numerical approximation of fixed point operator, particularly for the integral one associated to a nonlinear mixed Fredholm–Volterra integral equation, which uses the properties of rationalized Haar wavelets. The main tools for error analysis is Banach fixed point theorem. Furthermore, the order of convergence is analyzed. The algorithm to compute the solutions and some numerical examples are included to support the theory.
In this paper, we construct a new iterative method for solving nonlinear Volterra Integral Equation of the second kind, by approximating the Legendre polynomial basis. Error analysis is worked using property of interpolation. Finally, some examples are given to compare the results with some of the existing methods.
In this paper, we present a method for calculated the numerical approximation of nonlinear Fredholm - Volterra Hammerstein integral equation, which uses the properties of rationalized Haar wavelets. The main tool for error analysis is the Banach fixed point theorem. An upper bound for the error was obtained and the order of convergence is analyzed. An algorithm is presented to compute and illustrate the solutions for some numerical examples.
In this article we approximate the solutions of the nonlinear Fredholm integral equations of the second kind, by the method based on using the properties of RH wavelets and matrix operator. Also, the Banach fixed point theorem guarantees the convergence of the method. Also we get an upper bound for the error. Furthermore, the order of convergence is analyzed. The algorithm to compute the solutions and some numerical examples are also illustrated. The numerical results obtained by our method have been compared with other methods.
So far, there are no any publications for solving and obtaining a numerical solution of Volterra integro-differential equations in the complex plane by using the finite element method. In this work, we use the linear B-spline finite element method (LBS-FEM) and cubic B-spline finite element method (CBS-FEM) for solving this equation in the complex plane. We also discuss the error and convergence of the method. Furthermore, we give some numerical examples to substantiate efficiency of the proposed method.
In this article, using the properties of the rationalized Haar (RH) wavelets and the matrix operator, a method is presented for calculating the numerical approximation of the first Painlev\\\\\\\\\\\\\\\'e equations solution. Also, an upper bound of the error is given and by applying the Banach fixed point theorem the convergence analysis of the method is stated. Furthermore, an algorithm to solve the first Painlev\\\\\\\\\\\\\\\'e equation is proposed. Finally, the reported results are compared with some other methods to show the effectiveness of the proposed approach.
We consider a class of orthonormal quasi-wavelets and introduce quasi-wavelet method for solving Fredholm integral equations of the second kind in complex plane. We analyze the convergence of the anti-periodic quasi-wavelet method for solving linear Fredholm integral equation. The high accuracy and the wide applicability of APQWs approach is demonstrated with numerical example.
Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of non- linear Partial Dierential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Dier- ential Quadrature (DQ) method- based RBFs are applied to nd the numerical solution of the linear and nonlinear PDEs. The multiquadric (MQ) RBFs as basis function will introduce and applied to discretize PDEs. Dierential quadrature will introduce brie y and then we obtain the numerical solution of the PDEs. DQ is a numerical method for approximate and discretized partial derivatives of solution function. The key idea in DQ method is that any derivatives of unknown solution function at a mesh point can be approximated by weighted linear sum of all the functional values along a mesh line.
In this work, we used from 2D-Haar wavelet to approximate of nonlinear 2D Volterra – Fredholm Hammerstein integral equations. So, we define the integral operator, and obtain an operational matrix for our integral equation. we apply Banach fixed point theorem and we proved my integral operator has a unique fixed point. Finally, we solved some example with my method.
In this paper, an interval programming method is presented for solving unconstrained nonlinear fuzzy optimization problems where all the coefficients of the objective function are triangular fuzzy numbers. First, we convert unconstrained nonlinear fuzzy optimization problems unconstrained interval nonlinear programming problem by α-cuts. Then by solving the unconstrained interval nonlinear programming model, the optimal solution of the main problem will be obtained. To illustrate the proposed method numerical examples are solved and the obtained results are discussed.
We investigate mixed nonlinear integro-differential equations (MNIDEs) in general, utilizing the concept of rationalized Haar (RH) wavelet. The complexity of the MNIDE solution is known to everyone. For this purpose, we present a numerical method by applying the RH wavelet to approximate solutions of the MNIDE of the second kind in the complex plane. At first, we describe a continuous integral operator . Also, under mild assumptions, the Banach fixed point theorem ensures that the integral operator has a unique solution. Moreover, we give a result for error and compute the rate of convergence. Employing an algorithm, we present some illustrative examples to demonstrate the performance of this approach.
As far as we are aware, no research has been published about two-dimensional integral equations in the complex plane by using Haar bases or any other kinds of wavelets. We introduce a numerical method to solve two-dimensional Fredholm integral equations, using Haar wavelet bases. To attain this purpose, first, an operator and then an orthogonal projection should be defined. Regarding the characteristics of Haar wavelet, we solve an integral equation without using common mathematical methods. We prove the convergence and an upper bound that mentioned in the method by employing the Banach fixed point theorem. Moreover, the rate of convergence our method is O(n(2q)n). We present several examples of different kinds of functions and solve them by this method in this study.
In this paper, we propose a numerical scheme to solve a kind of nonlinear Fredholm integral equations of the second kind in the complex plane. The periodic quasi-wavelets (PQWs) constructed on [0; 2pi] are utilised as a basis of iteration method. Using the Banach fixed point theorem, we obtain some results concerning the error analysis. Illustrative examples are included to demonstrate the validity and applicability of the technique.
In the present research, we are going to obtain the solution of theWeapon-Target Assignment (WTA) problem. According to our search in the scientific reported papers, this is the first scientific attempt for resolving of WTA problem by projection recurrent neural network (RNN) models. Here, by reformulating the original problem to an unconstrained problem a projection RNN model as a high-performance tool to provide the solution of the problem is proposed. In continuous, the global exponential stability of the system was proved in this research. In the final step, some numerical examples are presented to depict the performance and the feasibility of the method. Reported results were compared with some other published papers.
Real life applications arising in various fields of engineering and science (e.g. electrical, civil, economics, dietary, etc.) can be modelled using a system of linear equations. In such models, it may happen that the values of the parameters are not known or they cannot be stated precisely and that only their estimation due to experimental data or experts knowledge is available. In such a situation it is convenient to represent such parameters by fuzzy numbers. In this paper we propose an efficient optimization model for obtaining a weak fuzzy solution to fuzzy linear systems (FLS). We solve some examples and we show that this method is always efficient.
We present a method for calculating the numerical approximation of the two-dimensional mixed Volterra Fredholm integral equations, using the properties of the rationalized Haar (RH) wavelets and the matrix operator. Attaining this purpose, first, an operator and then an orthogonal projection should be defined. Regarding the characteristics of Haar wavelet, we solve the integral equation without using common mathematical methods. An upper bound and the convergence of the mentioned method have been proved, by using the Banach fixed point. Moreover, the rate of the convergence method is O(n(2q)n). Finally, several examples of different kinds of functions are presented and solved by this method.
در این مقاله یک روش عددی بر مبنای تفاضلات متناهی برای حل مساله انتگرال-دیفرانسیل با مشتقات جزئی با هستهی منفرد ارائه شده است. ابتدا یک الگورتیم عددی برای حل مساله براساس طرح کرانک-نیکلسون با شرایط داده شده ارائه و سپس گسستهسازی انتگرال منفرد را برای حل این مساله به کار میبریم. در ادامه برای نشان دادن کارایی روش بیان شده با مقایسه جواب تقریبی و دقیق، با روش بیاسپلاین مکعبی نتیجه میگیریم که روش ارائه شده از دقت و کارائی لازم برخوردار میباشد. در ادامه شکل تقریبی نیز رسم شده است. سرعت بالای محاسبات، سهولت در بدست آمدن و اطمینان از داشتن جواب تقریبی به دلیل اثبات پایداری از مزایای این روش می باشد.
In this paper, numerical solutions of multiple cracks problems in an infinite plate are studied. Hypersingular integral equations (hieq) for the cracks are formulated using the complex potential method. For all kernels such as regular or hypersingular kernels, we are using the appropriate quadrature formulas to solve and evaluate the unknown functions numerically. Furthermore, by using this equation the stress intensity factor (SIF) was calculated for crack tips. For two serial cracks (horizontal) and two dissimilar cracks (horizontal and inclined), our numerical results agree with the previous works.
In this work, the rational Haar wavelet method has been used to solve the two-dimensional Volterra integral equations. Numerical solutions and the rate of convergence, are presented by applying a simple and efficient computational algorithm.
We study an SIS epidemic model with a constant recruitment. The disease-related death is included in the model and total population size is variable. A vaccination program also affects both new members and susceptible individuals. Two equilibria of the model; the disease-free equilibrium (DFE) and the endemic equilibrium (EE), and the basic reproduction number R 0 , are obtained. It is shown that DFE is locally and also globally asymptotically stable if R 0 < 1 . Furthermore, it is proven that EE is locally asymptotically stable when R 0 > 1 . In addition, in this case some conditions for global asymptotic stability of EE are found by using Lyapunov’s direct method. Finally, some numerical simulations are presented to verify obtained theoretical results.
this work, we used the properties of two-dimensional Haar wavelet, for this purpose it is required to define the integral operator, and obtain an operational matrix for our integral equation. Also, we used from 2D-Haar wavelet to approximate solutions of nonlinear two-dimensional Fredholm integral equations without any solving of linear system. In section error analysis, we apply Banach fixed point theorem and we proved my integral operator has a unique fixed point. In section four, numerical example we choose one example and we have compared my method with the other methods.
In this paper, we present a method for calculated the numerical approximation of nonlinear Fredholm - Volterra Hammerstein integral equation, which uses the properties of rationalized Haar wavelets. The main tool for error analysis is the Banach fixed point theorem. An upper bound for the error was obtained and the order of convergence is analyzed. An algorithm is presented to compute and illustrate the solutions for some numerical examples.
In this paper, the nite element method is used to approximate the solutions of the linear system of integrodifferential equations of the second kind has been considered. For this purpose we using the variational form. More ever, in the last section, some numerical examples are considered.
In this article we calculated the solutions of nonlinear Volterra Hammerstein integral equations of second kind, by uses the properties of rationalized Haar wavelets. The main tool for error analysis is using the Banach fixed point theorem and we get an upper bound for the error. Furthermore, the order of convergence is analyzed. The algorithm to compute the solutions and some numerical examples are also illustrated. The numerical results obtained by the our method have been compared with other methods.
In this paper, we suggest introduce a new and efficient numerical approach for solving of mixed 2D nonlinear Fredholm - Volterra integral equations. The fundamental structure of this method is based on the using of 2D Haar wavelet. Also, error analysis for method is presented by using the Banach xed point theorem, and this theorem guarantees that under certain assumptions, this equation has a unique xed point. Finally, some numerical examples are given to show the accuracy of the method, and results are compared with other numerical methods.
In this paper we have introduced a computational method for a class of two-dimensional nonlinear Fredholm integral equations,The method is based on2D Haar wavelet. Also, Banach fixed point theoremguarantees that under certain assumptions, this equation has a unique fixed point.Numerical examples are presented and results are compared with other numerical methods.