Ultraspherical Wavelets Method for Solving Lane-emden Type Equations
نویسندگان
چکیده
In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differential equations of Lane-Emden type are developed. The main idea for obtaining the presented algorithm is essentially based on reducing the linear or nonlinear equations with their initial conditions to systems of linear or nonlinear algebraic equations, which can be efficiently solved. Some numerical examples are given to demonstrate the validity and the applicability of the algorithms.
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