We prove quasioptimal and optimal order estimates in various Sobolev norms for the approximation of linear strongly elliptic pseudodifferential equations in one independent variable by the method of nodal collocation by odd degree polynomial splines. The analysis pertains in particular to many of the boundary element methods used for numerical computation in engineering applications. Equations ...

We consider nonlinear integral equations of Fredholm and Volterra type with respect to functions having values in L-spaces. Such class of equations includes set-valued integral equations, fuzzy integral equations and many others. We prove theorems of existence and uniqueness of the solutions for such equations and investigate data dependence of their solutions.

In this paper, continuous Legendre multi-wavelets are utilized as a basis in a practical direct method to approximate the solutions of the Fredholm integral equations system. To begin with we describe the characteristic of Legendre multi-wavelets and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Finally, numerica...

‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre ...

In this work, a functional approximation method for calculating the linear functional of the solution of second-kind Fredholm integral equations is developed. When the method is applied to the collocation method or to the multi-projection method, it generates approximations which exhibit superconvergence. © 2008 Elsevier Ltd. All rights reserved.

NEW ALGORITHMS FOR NUMERICAL SOLUTION OF NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF THIRD ORDER USING HAAR WAVELETS M. Fayyaz a and M. Azram b * Department of Computer Science, CECOS University Peshawar, Pakistan. [email protected] b Faculty of Engineering, IIUM, Kuala Lumpur 50728, Malaysia. [email protected] ABSTRACT: This paper deals with the extension of earlier work [3] (designed for Fre...

A numerical solution for solving non-linear Fredholm integral equations is presented. The method is based upon homotopy perturbation theory. The result reveal that the modified homotopy perturbation method (MHPM) is very effective and convenient. 2007 Elsevier Ltd. All rights reserved.

We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first-order linear differential operators on the real line. The applications we have in mind include linear stability problems associated with travelling wave solutions to nonlinear partial differential equations, for example reaction-diffusion or solitary wave equations. The...