Solution of a scaled system by shifted Legendre series representation

Abstract An elegant operational matrix which relates shifted Legendre polynomials to their scaled forms is derived. Based on this newly developed scale matrix and the existing operational matrix of integration, the shifted Legendre polynomials are applied to analyze a functional differential equation having terms with a scaled argument. The original functional differential equation is converted to a set of algebraic equations in unknown expansion coefficients, which can be solved recursively. Two numerical examples are included for illustration.