Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis

2021 ◽  
Vol 36 (1) ◽  
pp. 83-98
Author(s):  
K. Maleknejad ◽  
M. Soleiman Dehkordi
Keyword(s):  
Convergence Analysis ◽  
Integral Equations ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Nonlinear Integral Equations ◽  
Wavelet Method

Solving Two-Dimensional Nonlinear Volterra Integral Equations Using Rationalized Haar Functions in the Complex Plane

2020 ◽  
Vol 12 (3) ◽  
pp. 409-415
Author(s):  
Majid Erfanian ◽  
Hamed Zeidabadi ◽  
Rohollah Mehri
Keyword(s):  
Integral Equations ◽  
Order Of Convergence ◽  
Computational Algorithm ◽  
Numerical Solutions ◽  
Haar Wavelet ◽  
Volterra Integral Equations ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Haar Functions ◽  
Banach Theorem

In this work, two-dimensional rational Haar wavelet method has been used to solve the twodimensional Volterra integral equations. By using fixed point Banach theorem we achieved the order of convergence and the rate of convergence is O(n(2q)n). Numerical solutions of three examples are presented by applying a simple and efficient computational algorithm.

AN EFFICIENT NUMERICAL APPROACH FOR SOLVING ABEL’S INTEGRAL EQUATIONS BY USING MODIFIED TAYLOR WAVELETS

2021 ◽  
Vol 10 (5) ◽  
pp. 2285-2294
Author(s):  
A. Kumar ◽  
S. R. Verma
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Numerical Approach ◽  
Algebraic Equations ◽  
Wavelet Method

In this paper, a modified Taylor wavelet method (MTWM) is developed for numerical solutions of various types of Abel's integral equations. This method is based on the modified Taylor wavelet (MTW) approximation. The purpose behind using the MTW approximation is to transform the introduction problems into an equivalent set of algebraic equations. To check the accuracy and applicability of the proposed method, some examples have been solved and compared with other existing methods.

scholarly journals Numerical Solution for the 2D Linear Fredholm Functional Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Neda Khaksari ◽  
Mahmoud Paripour ◽  
Nasrin Karamikabir
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Unknown Function ◽  
Numerical Solutions ◽  
Functional Integral ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

In this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a finite series in terms of basic functions. Then, by using the proposed method, we give a formula for determining the unknown function. Using this formula, we obtain a numerical method for solving Fredholm two-dimensional functional linear integral equations. Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications.

Numerical Treatment of Nonlinear Stochastic Itô–Volterra Integral Equations by Piecewise Spectral-Collocation Method

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Fakhrodin Mohammadi
Keyword(s):  
Approximate Solution ◽  
Finite Number ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Lagrange Interpolation ◽  
Interpolation Method ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Treatment ◽  
Nonlinear Integral Equations

This paper deals with the approximate solution of nonlinear stochastic Itô–Volterra integral equations (NSIVIE). First, the solution domain of these nonlinear integral equations is divided into a finite number of subintervals. Then, the Chebyshev–Gauss–Radau points along with the Lagrange interpolation method are employed to get approximate solution of NSIVIE in each subinterval. The method enjoys the advantage of providing the approximate solutions in the entire domain accurately. The convergence analysis of the numerical method is also provided. Some illustrative examples are given to elucidate the efficiency and applicability of the proposed method.

Numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types)

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jiao Wang
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Numerical Algorithm ◽  
Numerical Solutions ◽  
Integral Transformation ◽  
Operational Matrix ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Content Type ◽  
Mixed Types

Purpose This paper aims to propose an efficient and convenient numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types). Design/methodology/approach The main idea of the presented algorithm is to combine Bernoulli polynomials approximation with Caputo fractional derivative and numerical integral transformation to reduce the studied two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations to easily solved algebraic equations. Findings Without considering the integral operational matrix, this algorithm will adopt straightforward discrete data integral transformation, which can do good work to less computation and high precision. Besides, combining the convenient fractional differential operator of Bernoulli basis polynomials with the least-squares method, numerical solutions of the studied equations can be obtained quickly. Illustrative examples are given to show that the proposed technique has better precision than other numerical methods. Originality/value The proposed algorithm is efficient for the considered two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations. As its convenience, the computation of numerical solutions is time-saving and more accurate.

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