Numerical Techniques for Second-Order Boundary Value Problems Utilizing Schröder Polynomials

Abstract

This study introduces novel numerical methods that employ spectral Galerkin and collocation techniques with shifted Schröder polynomials (SSPs) to solve linear and nonlinear second-order two-point boundary value problems (SOTBVPs). The proposed techniques are formulated through a reduced sequence of modified sets of SSPs. The unknown expansion coefficients are determined by using spectral Galerkin and collocation techniques. The resulting algebraic systems are efficiently solved using appropriate numerical solvers. Illustrative examples are provided to validate and demonstrate the accuracy, efficiency, and applicability of the proposed methodologies.