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• W2898926899 abstract "The use of finite difference approximations on geometric mesh network has been reported for the numerical estimation of two spatial dimensions mildly nonlinear elliptic boundary value problems with integral form of the source term. The new scheme applied the special type of unequal mesh spacing for differentials and integrals and obtained compact formulation for the mildly nonlinear equations. The estimated order of the scheme is three if the meshes are unequally spaced and achieves an accuracy of order four for evenly spaced mesh points. The necessary condition for the scheme to converge has been obtained with the help of monotonicity and irreducibility of the iteration matrix. The accuracy and efficiency of the proposed compact scheme have been illustrated using Helmholtz equation, stationary heat equation and steady-state mass transfer equation. The root mean squared error on the test problems with known true solutions justifies the third (four)-order accuracies of the new scheme. It is demonstrated that the third-order compact scheme on geometric meshes improves the efficiency and accuracy while comparing with fourth-order scheme on uniform mesh network." @default.
• W2898926899 created "2018-11-09" @default.
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• W2898926899 date "2018-10-31" @default.
• W2898926899 modified "2023-09-23" @default.
• W2898926899 title "A Third-Order Accurate Finite Difference Method and Compact Operator Approach for Mildly Nonlinear Two Spatial Dimensions Elliptic BVPs with Integral Form of Source Term" @default.
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• W2898926899 doi "https://doi.org/10.1007/978-981-13-1595-4_71" @default.
• W2898926899 hasPublicationYear "2018" @default.
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