The Laplace Transform Multiquadric Method: A Highly Accurate Scheme for the Numerical Solution of Partial Differential Equations

We combine the numerical inversion of Laplace Transforms to integrate partial differential equations (PDEs) in time, with an exponentially-convergent grid-free spatial approximation scheme called multiquadrics (MQ) for the spatial terms. The new method yields remarkably accurate numerical solutions, and the computational effort holds the promise of being orders of magnitude more efficient than traditional finite difference (FD) or finite element (FE) methods.

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