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Call for Paper - December – 2022 Edition   

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IJATCA solicits original research papers for the December – 2022 Edition.
Last date of manuscript submission is December 30, 2022.

                                                   

Numerical Solution of Coupled system of Boundary value problems by Galerkin method with different order B-splines


Volume: 1 Issue: 1
Year of Publication: 2019
Authors: Murali Krishna Panthangi, Dhivya C.



Abstract

In the current paper, we present a Galerkin method with cubic, quarticB-splines for the numerical solution of highly coupled system of nonlinear boundary value problems (BVP).The method is actually applied on a linearized form of given BVP. For linearization, we used quasi linearization technique to convert the given nonlinear BVP into a sequence of linear BVPs. For each linear BVP, each unknown variable is approximate by a linear combination of cubic B-splines or quartic B-splines depending on the order of derivative for the variable that is present in the given BVP. For a variable with third order derivative present in given BVP, we used quartic B-splines where as for the variables with second order derivative, we used cubic B-splines in the approximation. Galerkin method was employed with these approximations and hence obtained the results. The convergence criterion for the solution of sequence of linear BVP is fixed at 1.0〖10〗^(-5). To test the efficiency of the proposed method, we employed the presented method on a problem which is available in the literature. Numerical results obtained by the proposed method are in with good agreement with the results available in the literature for the tested problem.

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Keywords

Coupled nonlinear boundary value problem, Galerkin method, B-spline, Numerical solution




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