Novel Functional Matrix Method using Standard Basis of Polynomial Linear Space

Abstract

This paper has developed a novel functional matrix using the standard basis of (n+1) dimensional polynomial linear space to solve second-order singular initial and boundary problems. The linearly independent polynomials properties are used to convert the differential equations into algebraic equations with suitable solvers that can efficiently solve. Seven numerical examples are considered to demonstrate this technique's applicability and efficiency. The obtained results are compared favorably with the exact solutions. Also, we proved some theorems on convergence, exact solutions, and uniform convergence