Two-Point Boundary Problems with One Mild Singularity and an Application to Graded Kirchhoff Plates

TL;DR

This paper introduces a new algebraic method for solving boundary value problems with mild singularities at one endpoint, demonstrated through an application to graded Kirchhoff plates.

Contribution

It develops a novel algebraic framework for linear ODE boundary problems with singularities, implemented in Theorema, and applies it to graded Kirchhoff plates.

Findings

Successful algebraic treatment of singular boundary problems

Implementation in Theorema software system

Application to graded Kirchhoff plates

Abstract

We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic approach, with (partial) implementation in the Theorema software system (which is based on Mathematica). We study an application to graded Kirchhoff plates for illustrating a typical case of such boundary problems.