Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD)...

An investigation into the dynamic characterisation of a rectangular flexible plate structure is presented and a simulation algorithm characterising the behaviour of the plate is developed using finite difference methods. A thin, rectangular plate, with all edges clamped, is considered. The investigation is accomplished by varying the width over the length ratio of the plate. The algorithm is im...

In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions for their stab...

Time finite element methods are developed for the equations of structural dynamics. The approach employs the time-discontinuous Galerkin method and incorporates stabilizing terms having least-squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time-discontinuous Galerkin and l...

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We study a superreplication problem of European options with gamma constraints, in mathematical finance. The initially unbounded control problem is set back to a problem involving a viscosity PDE solution with a set of bounded controls. Then a numerical approach is introduced, inconditionnally stable with respect to the mesh steps. A generalized finite difference scheme is used since basic fini...

Thirdand fourth-order accurate finite difference schemes for the first derivative of the square of the speed are developed, for both uniform and non-uniform grids, and applied in the study of a two-dimensional viscous fluid flow through an irregular domain. The von Mises transformation is used to transform the governing equations, and map the irregular domain onto a rectangular computational do...

Finite difference method is used to calculate the via-plate capacitances for vias with pad. Due to the symmetric structure, the solving domain is reduced to a rectangular ρ − z region. Boundary conditions along the region are discussed. Both barrel-plate and pad-plate capacitances are studied with various geometric parameters. The results could be used as validations for possible analytical exp...

Discrete versions of basic inequalities in functional analysis such as the Sobolev inequality play key role in theoretical analysis of finite difference schemes. They have been shown for some simple difference operators, but are still left open for general operators, even including the standard central difference operators. In this paper, we propose a systematic approach for deriving such inequ...

we put forward a new migration imaging technique of Magnetotellurics (MT) data based on improved finite difference method, which increased the accuracy of difference equation and imaging resolution greatly. We also discussed the determination of background resistivity and reimaging. The processing results of theoretical model and case study indicated that this method was a more practical and ef...