Legendre collocation method for solving nonlinear differential equations
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Date
2013
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Abstract
In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomials. The method by means of Legendre collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Legendre coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparisons are made between the obtained solution and the exact solution.
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Mathematical transformations , Matrix algebra , Numerical methods , Ordinary differential equations , Polynomials , Riccati equations , Approximate solution , Legendre coefficient , Legendre collocations , Legendre polynomials , Legendre-collocation method , Nonlinear algebraic equations , Nonlinear differential equation , Nonlinear ordinary differential equation , Nonlinear equations