121 research outputs found
Theory of block-pulse functions in numerical solution of Fredholm integral equations of the second kind
Wavelet analysis method for solving linear and nonlinear singular boundary value problems
In this paper, a robust and accurate algorithm for solving both linear and nonlinear singular boundary value problems is proposed. We introduce the Chebyshev wavelets operational matrix of derivative and product operation matrix. Chebyshev wavelets expansions together with operational matrix of derivative are employed to solve ordinary differential equations in which, at least, one of the coefficient functions or solution function is not analytic. Several examples are included to illustrate the efficiency and accuracy of the proposed method
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A modification of pseudo-spectral method for solving a linear ODEs with singularity
In this paper, first we introduce, briefly, pseudo-spectral method for numerical solution of ODE’s and focus on those problems in which some of coefficient functions or solution function are singular. Then, by expressing weak and strong aspects of spectral methods to solve these kind of problems, a modified pseudo-spectral method which is more efficient than other spectral methods is suggested. We compare the methods with some numerical examples
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