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The current study is presented to develop two approaches and methodologies to find the numerical solution of linear and non-linear initial value problems such as Lane–Emden type equation, Riccati’s equation and Bessel’s equation of order zero based on approximation. The function approximations (scheme-I and scheme-II) are presented to find the numerical solutions of linear and non-linear initial value...
In this article, we have study a 2D Legendre and Chebyshev wavelets collocation scheme for solving a class of linear and nonlinear weakly singular Volterra partial integro-differential equations (PIDEs). The scheme is based on wavelets collocation for PIDEs with uniquely designed matrices over the Hilbert space defined on the domain $$\left( [0, 1]\times [0, 1]\right) $$ [0,1]×[0,1] . Using piecewise...
This paper deals with an approximate analytical solution of multi-dimensional, time-fractional coupled viscous Burgers’ equation obtained by employing “homotopy perturbation method” where fractional derivative is of Caputo type. Three test problems are carried out in order to validate and illustrate the efficiency of the method for TFCB equation. The results are also depicted in graphically for different...
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