This paper presents the Jeffery Hamel flow of a non-Newtonian fluid namely Casson fluid. Suitable similarity transform is applied to reduce governing nonlinear partial differential equations to a much simpler ordinary differential equation. Variation of Parameters Method (VPM) is then employed to solve resulting equation. Same problem is solved numerical by using Runge-Kutta order 4 method. A c...

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi‐ step integration methods. The coefficients are reverse engineered based on samples from a target function and its derivative used for training. The Runge‐Kutta schemes are tra...

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge–Kutta method having stage order four. Themethod thus obtained have good properties relatives to stability including an unboun...

New Runge–Kutta methods for method of lines solution of systems of ordinary differential equations arising from discretizations of spatial derivatives in hyperbolic equations, by Chebyshev or modified Chebyshev methods, are introduced. These Runge–Kutta methods optimize the time step necessary for stable solutions, while holding dispersion and dissipation fixed. It is found that maximizing disp...

In this talk, we devise a new Runge-Kutta Discontinuous Galerkin (RKDG) method that achieves full high-order convergence in time and space while keeping the timestep proportional to the spatial mesh-size. To this end, we derive an extension to non-autonomous linear systems of the mth-order, m-stage strong stability preserving Runge-Kutta (SSP-RK) scheme with low storage described in Gottlieb et...