RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function

Abstract This work concerns the weights of the radial basis function generated finite difference (RBF-FD) formulas for estimation of the first and second derivatives of an unknown function applying the generalized multiquadric function (GMQ). Several discussions about their error equations on structured and unstructured grids of points are worked out. Next, the formulas are applied on a new non-uniform mesh of points based on modified Legendre polynomial zeros in order to computationally solve a (1+2) dimensional partial integro-differential equation (PIDE) arising in the model of stochastic volatility with contemporaneous jumps (SVCJ). Numerical results show a fast convergence for solving this problem.

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