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An application of Zakian inversion method in solving hyperbolic differential equations. (Chinese. English summary) Zbl 1299.65251

Summary: By means of the Laplace transformation, the hyperbolic differential equations are transformed to elliptic differential equations which can be solved by the fourth order finite difference scheme in parallel. After getting the approximate solutions of the elliptic differential equations, we can achieve the numerical solutions with high accuracy in any time for the hyperbolic differential equations by using the Zakian inversion method. At last, we carry out one numerical experiment to indicate that the method in this paper is very effective.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N06 Finite difference methods for boundary value problems involving PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A10 Laplace transform
35L20 Initial-boundary value problems for second-order hyperbolic equations
35J25 Boundary value problems for second-order elliptic equations
65Y05 Parallel numerical computation
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