High order convergent modified nodal bi-cubic spline collocation method for elliptic partial differential equation |
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Authors: | Suruchi Singh Swarn Singh |
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Institution: | 1. Department of Mathematics, Aditi Mahavidyalaya, University of Delhi, New Delhi, India;2. Department of Mathematics, Sri Venkateswara College, University of Delhi, New Delhi, India |
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Abstract: | A high order modified nodal bi-cubic spline collocation method is proposed for numerical solution of second-order elliptic partial differential equation subject to Dirichlet boundary conditions. The approximation is defined on a square mesh stencil using nine grid points. The solution of the method exists and is unique. Convergence analysis has been presented. Moreover, the superconvergent phenomena can be seen in proposed one step method. The numerical results clearly exhibit the superiority of the new approximation, in terms of both accuracy and computational efficiency. |
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Keywords: | collocation convergence cubic spline interpolation elliptic partial differential equation high order |
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