The application of block pulse functions for solving higher-order differential equations with multi-point boundary conditions

Advances in Difference Equations

Mohammad Heydari¹  Zakieh Avazzadeh² 

[1] Department of Mathematics, Yazd University, Yazd, Iran;Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China

关键词: ordinary differential equations;    block pulse functions;    boundary value problem;    multi-point value problem;    separated or non-separated boundary conditions;    65Lxx;    94A11;    34k28;   

DOI  :  10.1186/s13662-016-0822-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the block pulse function method is proposed for solving high-order differential equations associated with multi-point boundary conditions. Although the orthogonal block pulse functions frequently have been applied to approximate the solution of ordinary differential equations associated with the initial conditions, the presented method provides the flexibility with respect to multi-point boundary conditions in separated or non-separated forms. This technique, which may be named the augmented block pulse function method, reduces a system of high-order boundary value problems of ordinary differential equations to a system of algebraic equations. The illustrated results confirm the computational efficiency, reliability, and simplicity of the presented method.

【 授权许可】

CC BY