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This paper deals with ADI type schemes in the numerical solution of the large systems of stiff ODEs that arise after spatial discretization of the Heston PDE from financial option pricing. A feature of this well-known two-dimensional PDE is the presence of a mixed spatial derivative term, and ADI schemes were not originally developed to handle such terms. We discuss how to adapt three ADI schemes and next we review theoretical results and perform numerical experiments. [ABSTRACT FROM AUTHOR]

A simple elliptic equation method is used for constructing exact trevelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. With the aid of Maple, more new travelling solitary wave and periodic solutions are obtained for the generalized Kawahara equation. [ABSTRACT FROM AUTHOR]

We fully utilize Peano kernels theorem to the error estimates of bivariate self-validating integration based on product cubature rules. This application enable adaptive local error estimates. We demonstrate the characteristics and effectiveness of our methods by comparing it with a conventional integrator. [ABSTRACT FROM AUTHOR]