Approximate solutions for a class of nonlinear Volterra-Fredholm integro-differential equations under Dirichlet boundary conditions

AIMS Mathematics

article

Hawsar Ali Hama Rashid¹  Mudhafar Fattah Hama² 

[1] College of Education- Department of Mathematics, University of Sulaimani;College of Science- Department of Mathematics, University of Sulaimani

关键词: boundary value problem;    integro-differential equations;    existence;    uniqueness;    modified Adomian's decomposition method;    homotopy analysis method;   

DOI  :  10.3934/math.2023022

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

This paper studies the solvability of boundary value problems for a nonlinear integro-differential equation. Converting the problem to an equivalent nonlinear Volterra-Fredholm integral equation (NVFIE) is driven by using a suitable transformation. To investigate the existence and uniqueness of continuous solutions for the NVFIE under certain given conditions, the Krasnoselskii fixed point theorem and Banach contraction principle have been used. Finally, we numerically solve the NVFIE and study the rate of convergence using methods based on applying the modified Adomian decomposition method, and Liao's homotopy analysis method. As applications, some examples are provided to support our work.

【 授权许可】

CC BY