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

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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.

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