The refinement-schemes-based unified algorithms for certain nth order linear and nonlinear differential equations with a set of constraints

Syeda Tehmina Ejaz,Yu-Ming Chu,Ghulam Mustafa,Dumitru Baleanu

doi:10.1186/s13662-021-03283-2

Abstract

We first present a generalized class of binary interpolating refinement schemes and their properties. Then the refinement-schemes-based unified algorithms for the solution of certain nth order linear and nonlinear differential equations with a set of constraints are presented. Moreover, several algorithms based on the refinement schemes for solving differential equations are the special cases of our algorithms.

Highlights

The refinement schemes, known as subdivision schemes, are efficient tools for the modeling of curves
We present generalized algorithms based on generalized refinement schemes for the nth order linear and nonlinear differential equations (DEs)
All the subdivision-based algorithms are restructured by substituting the suitable values of n and m in generalized algorithms for the solution of the nth order linear and nonlinear differential equations with a set of constraints

Summary

Introduction

The refinement schemes, known as subdivision schemes, are efficient tools for the modeling of curves. In 1996, initially, Qu and Agarwal [2] presented a refinement-scheme-based algorithm for the second-order linear differential equations (DEs). 3.1 Generalized algorithm for the nth order linear DEs we construct the refinement-scheme-based algorithm for the nth order linear DEs. Let the solution of (3) be. 3.2 Generalized algorithm for the nth order nonlinear DEs In this subsection, we construct the refinement-scheme-based algorithm for the nth order nonlinear DEs. Let the solution of (4) be GNL(t) =.

The left end imposed constraints

Existence of the solution

The special cases of our algorithms based on approximating schemes

Conclusion