Compact Schemes for the Spatial Discretization of Linear Elliptic Partial Differential Equations
E. Dhananjaya1, R. Bhuvana Vijaya2
1E. Dhananjaya, Research Scholar, Jawaharlal Nehru Technological University Anantapur, Ananthapuramu, Andhra Pradesh, India.
2R. Bhuvana Vijaya, Professor and Head, Department of Mathematics, Jawaharlal Nehru Technological University Anantapur, Ananthapuramu, Andhra Pradesh, India.
Manuscript received on January 14, 2020. | Revised Manuscript received on January 21, 2020. | Manuscript published on February 10, 2020. | PP: 1529-1535 | Volume-9 Issue-4, February 2020. | Retrieval Number: D1695029420/2020©BEIESP | DOI: 10.35940/ijitee.D1695.029420
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Abstract: IA system of compact schemes used, to approximate the partial derivative 2 2 1 f x and 2 2 2 f x of Linear Elliptic Partial Differential Equations (LEPDE) ,on the non-boundary nodes, located along a particular horizontal grid line for 2 2 1 f x and along a particular vertical grid line for 2 2 2 f x of a two-dimensional structured Cartesian uniform grid. The aim of the numerical experiment is to demonstrate the higher order spatial accuracy and better rate of convergence of the solution, produced using the developed compact scheme. Further, these solutions are compared with the same, produced using the conventional 2 nd order scheme. The comparison is made, in terms of the discrete l l 2 & norms, of the true error. The true error is defined as, the difference between the computed numerical and the available exact solution, of the chosen test problems. It is computed on every non-boundary node bounded in the computational domain.
Keywords: Fourth order Central Difference based Compact schemes, Spatial Discretization, Linear Elliptic Partial Differential Equations, Incompressible fluid flow, Explicit Scheme, Implicit Scheme e.
Scope of the Article: Fluid Mechanics