Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations (original) (raw)
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CAUCHY Journal, 2020
In this paper, a matrix approach to the direct computation method for solving Fredholm Integro-Differential Equations (FIDEs) of the second kind with degenerate kernels is presented. Our approach consists of reducing the problem to a set of linear algebraic equations by approximating the kernel with a finite sum of products and determining the unknown constants by the matrix approach. The proposed method is simple, efficient and accurate; it approximates the solutions exactly with the closed form solutions. The result of this research is the solution of the second type Fredholm integro-differential equation (FIDE) with a numerically accurate kernel degenerate. Some problems are considered using maple programme to illustrate the simplicity, efficiency and accuracy of the proposed method.
An Appropriate Numerical Method for Solving Nonlinear Volterra-Fredholm Integral Equations
International Journal of Mathematics and Systems Science, 2018
This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.