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Four step implicit block method of Runge-Kutta type for solving first order ordinary differential equations

Hazwani Mohd Radzi, Zanariah Abdul Majid, Fudziah Ismail, Mohamed Suleiman

Open publisher page 8 citations

Abstract

In this paper, a four step implicit block method for solving first order ordinary differential equations (ODEs) is proposed. The method approximates the solutions of initial value problems at four-point mesh simultaneously using variable step size. This four step implicit method is of the multistep type but it is implemented as the Runge-Kutta type. The stability regions of the method are also studied. Numerical results are presented to show the efficiency of the proposed block method.

About this research paper

What this paper is about

In this paper, a four step implicit block method for solving first order ordinary differential equations (ODEs) is proposed. The method approximates the solutions of initial value problems at four-point mesh simultaneously using variable step size. This four step implicit method is of the multistep type but it is implemented as the Runge-Kutta type. The stability regions of the method are also studied. Numerical results are presented to show the efficiency of the proposed block method.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, a four step implicit block method for solving first order ordinary differential equations (ODEs) is proposed. The method approximates the solutions of initial value problems at four-point mesh simultaneously using variable step size. This four step implicit method is of the multistep type but it is implemented as the Runge-Kutta type. The stability regions of the method are also studied. Numerical results are presented to show the efficiency of the proposed block method.

Key concepts: Runge–Kutta methods, Linear multistep method, Ordinary differential equation, Numerical methods for ordinary differential equations, Explicit and implicit methods, L-stability, Mathematics, Ode

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