The Multistage Differential Transform Method (MDTM) is employed to solve the model for HIV infection of CD4T cells. Comparing the numerical results to those obtained by the classical fourth order Runge-Kutta method showed the preciseness and efficacy of the multistep differential transform method. The study shows that the method is a powerful and promising tool for solving coupled systems of di...

Radial basis function-Pseudospectral method and Fourier Pseudospectral (FPS) method are extended for stiff nonlinear partial differential equations with a particular emphasis on the comparison of the two methods. Fourth-order Runge-Kutta scheme is applied for temporal discretization. The numerical results indicate that RBF-PS method can be more accurate than standard Fourier pseudospectral meth...

We investigate efficient algorithms and a practical implementation of an explicittype high-order timestepping method based on Krylov subspace approximations, for possible application to large-scale engineering problems in electromagnetics. We consider a semi-discrete form of the Maxwell’s equations resulting from a high-order spectral-element discontinuous Galerkin discretization in space whose...

We present new symmetric fourth and sixth-order symplectic Partitioned Runge{ Kutta and Runge{Kutta{Nystrr om methods. We studied compositions using several extra stages, optimising the eeciency. An eeective error, E f , is deened and an extensive search is carried out using the extra parameters. The new methods have smaller values of E f than other methods found in the literature. When applied...

The application of fourth-order finite difference discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined further. In the bulk of the diffusion space, a central 5-point scheme is used, and 6-point asymmetric schemes are used at the edges. In this paper, four Runge-Kutta schemes have been used for ...

We analyze explicit Runge–Kutta schemes in time combined with stabilized finite elements in space to approximate evolution problems with a first-order linear differential operator in space of Friedrichs-type. For the time discretization, we consider explicit secondand third-order Runge–Kutta schemes. We identify a general set of properties on the spatial stabilization, encompassing continuous a...

We consider a machine repair problem with server breakdowns, in which an unreliable server (repairman) operates the threshold recovery policy. When there are no failed machines in the system, the server leaves for a vacation. If the server returns from a vacation to find no failed machines in the system, he/she immediately takes another vacation. And the server continues in this manner until he...

INCORPORATING KRYLOV SUBSPACE METHODS IN THE ETDRK4 SCHEME by Jeffrey H. Allen The University of Wisconsin–Milwaukee, 2014 Under the Supervision of Professor Bruce Wade A modification of the (2, 2)-Padé algorithm developed by Wade et al. for implementing the exponential time differencing fourth order Runge-Kutta (ETDRK4) method is introduced. The main computational difficulty in implementing th...