Modification of the Lagrange Interpolating Polynomial Scheme for Using with the Finite Difference Method

Modification of the Lagrange interpolating polynomial (LIP) scheme for using with the finite difference method is proposed. Merits of the modified LIP scheme used with the finite difference method for problem solving are facile to discretize equations, and fast to obtain solutions. Verification of the modified LIP scheme was performed by comparison of the solutions computed from the modified LIP scheme with the analytical solutions of a heat conduction problem. The verification gives credence to the modified LIP scheme for correctness of the solutions. In addition, the comparison results of solution accuracy and computational time of problem solving between using of the finite difference method with the modified LIP scheme and the finite volume method with the LIP scheme are exhibited.

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