in this paper, homotopy perturbation method (hpm) has been applied to investigate the effect of magnetic field on cu-water nanofluid flow in non-parallel walls. the validity of hpm solutions were verified by comparing with numerical results obtained using a fourth order runge–kutta method. effects of active parameters on flow have been presented graphically. the results show that velocity in bo...

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of ef...

in this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. for the time integration of the problem, the runge–kutta and spline-based differential quadrature methods have been applied. the runge–kutta method was unstable for solving the prob...

Recently an implicit method has been presented for solving first order singular initial value problem. The method is extended to solve second or higher order problems having a singular point. The method presents more correct result than those obtained by the implicit Euler and second order implicit Runge-Kutta (RK2) methods. The method is illustrated by suitable examples.

A new Runge-Kutta-Nyström method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this paper. The new method is based on the Dormand and Prince RungeKutta-Nyström method of algebraic order four[1]. Numerical illustrations indicate that the new method is much more efficient than the classical one.

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stag...

In the context of solving nonlinear partial differential equations, Shu and Osher introduced representations of explicit Runge-Kutta methods, which lead to stepsize conditions under which the numerical process is totalvariation-diminishing (TVD). Much attention has been paid to these representations in the literature. In general, a Shu-Osher representation of a given Runge-Kutta method is not u...

Generalized Fitzhugh– Nagumo equation; Polynomial differential quadrature method; Numerical solutions; Runge–Kutta method Abstract In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces the problem into a system of first order...