Trigonometrically-fitted Higher Order Two Derivative Runge-Kutta Method for Solving Orbital and Related Periodical IVPs

Embedded 5(4) Pair Trigonometrically-Fitted Two Derivative Runge- Kutta Method with FSAL Property for Numerical Solution of Oscillatory Problems

Based on First Same As Last (FSAL) technique, an embedded trigonometrically-fitted Two Derivative Runge-Kutta method (TDRK) for the numerical solution of first order Initial Value Problems (IVPs) is developed. Using the trigonometrically-fitting technique, an embedded 5(4) pair explicit fifth-order TDRK method with a “small” principal local truncation error coefficient is derived. The numerical...

An Embedded 4(3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Method for Solving Periodic Initial Value Problems

Embedded diagonally implicit Runge-Kutta-Nystrom 4(3) pair for solving special second-order IVPs

Abstract In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourthorder 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standar...

Trigonometrically-fitted second derivative method for oscillatory problems

ABSTRACT A continuous Trigonometrically-fitted Second Derivative Method (CTSDM) whose coefficients depend on the frequency and stepsize is constructed using trigonometric basis functions. A discrete Trigonometrically-fitted second derivative method (TSDM) is recovered from the CTSDM as a by-product and applied to solve initial value problems (IVPs) with oscillating solutions. We discuss the sta...

Nonstandard explicit third-order Runge-Kutta method with positivity property

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...