No abstract

No abstract

In this paper, we will give some results for developing the two-dimensional triangular orthogonal functions (2D-TFs) for numerical solution of the linear two-dimensional Fredholm integral equations of the second kind. The product of 2D-TFs and some formulas for calculating definite integral of them are derived and utilized to reduce the solution of two-dimensional Fredholm integral equation to the solution of algebraic equations. Also a theorem is proved for convergence analysis. Numerical examples are presented and results are compared with analytical solution to demonstrate the validity and applicability the method.

No abstract

Purpose -The purpose of this paper is to develop rationalized Haar functions to approximate the solutions of the integro-differential equations. Design/methodology/approach -Properties of rationalized Haar functions are first presented, and the operational matrix of the product of two rationalized Haar functions vector is utilized to reduce the computation of integro-differential equations to some algebraic equations. Findings -Numerical results support the theoretical results. Originality/value -Presents a method for solving integro-differential equations.

No abstract

No abstract

KEYWORDS error analysis, operational matrix method, singular integral equation, two-dimensional orthonormal Bernstein polynomials Numer Methods Partial Differential Eq. 2019;35:615-637. wileyonlinelibrary.com/journal/num