Comparative Study on Results of Euler, Improved Euler and Runge-Kutta Methods for Solving the Engineering Unknown Problems

Exponential Runge-Kutta methods for parabolic problems

The aim of this paper is to construct exponential Runge-Kutta methods of collocation type and to analyze their convergence properties for linear and semilinear parabolic problems. For the analysis, an abstract Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities is chosen. This framework includes interesting examples like reaction-diffusion equations. It...

Stochastic Diffusion Problems: Comparison Between Euler-Maruyama and Runge-Kutta Schemes

Using a class of stochastic Euler and Runge-Kutta methods, we numerically solve a reaction-diffusion equation with additive random excitation. By discretizing the space and the associated stochastic differential system, we present a comparison of the diffusibility behaviors between the schemes above. The model presented here consists of reaction-diffusion equations describing the evolution of t...

Theory and Implementation of Numerical Methods Based on Runge-kutta Integration for Solving Optimal Control Problems

Improved Runge-Kutta Methods for Solving Ordinary Differential Equations (Penambahbaikan Kaedah Runge-Kutta untuk Menyelesaikan Persamaan Pembezaan Biasa)

In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical RungeKutta method. Therefore the new scheme is computationally more efficient at achieving the same order of local accuracy. The order conditions of the new methods...

Theory and Implementation of Numerical Methods Based on Runge-Kutta Integration for Solving Optimal Control Problems

THEORY AND IMPLEMENTATION OF NUMERICAL METHODS BASED ON RUNGE-KUTTA INTEGRATION FOR SOLVING OPTIMAL CONTROL PROBLEMS