In this paper we study a class of explicit pseudo two-step Runge-Kutta (EP-TRK) methods for rst-order ODEs for parallel computers. We investigate linear stability and derive methods with enlarged stability regions. In numerical experiments on a shared memory computer we compare a parallel variable step size EPTRK implementation with the eecient sequential Runge-Kutta method dopri5.

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...

To my beautiful wife, Ashley. For your unconditional love, faithful encouragement, and resolute support. You have always believed in and inspired the pursuit of my dreams. iv ACKNOWLEDGEMENTS I would first like to express my immense gratitude to my advisor, Dr. Glenn Sjoden. What started as an undergraduate summer research project transformed into my path in graduate school. As both an advisor ...

Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed ...

This study utilised positive Lyapunov exponents’ criteria to develop chaos diagram on the parameters space of 4-dimensional harmonically excited vibration absorber control Duffing’s Oscillator. Relevant simulations were effected by choice combination of constant step Runge-Kutta methods and Grahm Schmidt Orthogonal rules. Simulations of 4-dimensional hyper-chaotic models of modified Lorenz and ...

In this paper we study numerical methods for Hybrid Fuzzy Differential equations by an appllication of the Runge-kutta Fehlberg method for fuzyy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.