Numerical solution of nonlinear partial differential equations using shifted Legendre collocation method

Abstract In life important applications are modeled mathematically by nonlinear partial differential equations. Primarily, the objective is to transform such equations into a system of algebraic equations to get their solutions. The Legendre collocation method is demonstrated by the differentiation operational matrix via shifted Legendre polynomials in such a transformation. The validity and effectiveness of the prospective method are manifested by illustrative examples, an error analysis, residual analysis, and comparison with others.