Operator splitting kernel based numerical method for a generalized Leland's model

We construct a first order in time and second order in space, positivity preserving numerical method for a generalized Hoggard-Whalley-Wilmott, Leland's model. We develop the hyperbolic-parabolic operator splitting method, using a kernel based algorithm for the parabolic part and van Leer flux limiter approach for the hyperbolic sub-problem. Properties of the proposed algorithms are discussed. Various numerical examples confirm the efficiency of the proposed method and verify the theoretical statements.

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