An optimized explicit low-storage fourth-order Runge–Kutta algorithm is proposed in the present work for time integration. Dispersion and dissipation of the scheme are minimized in the Fourier space over a large range of frequencies for linear operators while enforcing a wide stability range. The scheme remains of order four with nonlinear operators thanks to the low-storage algorithm. Linear a...

We study the performance of methods of lines combining discontinuous Galerkin spatial discretizations and explicit Runge-Kutta time integrators, with the aim of deriving optimal Runge-Kutta schemes for wave propagation applications. We review relevant Runge-Kutta methods from literature, and consider schemes of order q from 3 to 4, and number of stages up to q + 4, for optimization. From a user...

Sugiura, H. and T. Torii, A method for constructing generalized Runge-Kutta methods, Journal of Computational and Applied Mathematics 38 (1991) 399-410. In the implementation of an implicit Runge-Kutta formula, we need to solve systems of nonlinear equations. In this paper, we analyze the Newton iteration process and a modified Newton iteration process for solving these equations. Then we propo...

In this paper, a hybrid technique of differential quadrature method and Runge-Kutta fourth order method is employed to analyze reaction-diffusion problems. The obtained results are compared with the available analytical ones. Further, a parametric study is introduced to investigate the influence of reaction and diffusion characteristics on behavior of the obtained results. Index Term-Reaction-d...

we present here the numerical solution of damped forced oscillator problem using haar wavelet and compare the numerical results obtained with some well-known numerical methods such as runge-kutta fourth order classical and taylor series methods. numerical results show that the present haar wavelet method gives more accurate approximations than above said numerical methods.

In this paper, we classified a class of fourth-order partial differential equations (PDEs) to be fourth-order PDE of type I, II, III and IV. The PDE of type IV is solved by using an efficient numerical method. The PDE is first transformed to a system of fourth-order ordinary differential equations (ODEs) using the method of lines, then the resulting system of fourth-order ODEs is solved using d...

A fourth-order, implicit, low-dispersion, and low-dissipation Runge-Kutta scheme is introduced. The scheme is optimized for minimal dissipation and dispersion errors. High order accuracy is achieved with fewer stages than standard explicit Runge-Kutta schemes. The scheme is designed to be As table for highly stiff problems. Possible applications include wall-bounded flows with solid boundaries ...