Abstract
A novel compact scheme based on finite difference discretizations and geometric grid has been developed to solve two-dimensional mildly non-linear elliptic equations in polar co-ordinate constituting singular terms. The formula allows a most stable discretization and nine-point geometric stencils, thus arriving at a compact formulation. In general, a third order of magnitude has been accomplished and the fourth order of magnitude to the truncation error will be considered as a specific case. A precise error analysis for the suggested scheme was carried out on the basis of irreducible and strongly connected behavior of the Jacobian matrix. The essence of implementing geometric grid parameters has been shown with the help of numerical results. The numerical scheme has been applied to test Poisson equation, Helmholtz equation, Grad–Shafranov equation and a semi-linear elliptic equations in polar coordinate. The illustrative results corroborate the theoretical order of magnitude and accuracy of the method.
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