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2013•Mathematical theory and modelingRequires access

Development of Implicit Rational Runge-Kutta Schemes for Second Order Ordinary Differential Equations

S Usman Abdullahi, Saleh M. Hassan

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Abstract

In this paper, the development of One – Stage Implicit Rational Runge – Kutta methods are considered using Taylor and Binomial series expansion for the direct solution of general second order initial value problems of ordinary differential equations with constant step length. The basic properties of the developed method were investigated and found to be consistent and convergent. Keywords: Implicit Rational Runge Kutta scheme, Second Order Equations, Convergence and Consistent

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What this paper is about

In this paper, the development of One – Stage Implicit Rational Runge – Kutta methods are considered using Taylor and Binomial series expansion for the direct solution of general second order initial value problems of ordinary differential equations with constant step length. The basic properties of the developed method were investigated and found to be consistent and convergent. Keywords: Implicit Rational Runge Kutta scheme, Second Order Equations, Convergence and Consistent

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Available abstract

In this paper, the development of One – Stage Implicit Rational Runge – Kutta methods are considered using Taylor and Binomial series expansion for the direct solution of general second order initial value problems of ordinary differential equations with constant step length. The basic properties of the developed method were investigated and found to be consistent and convergent. Keywords: Implicit Rational Runge Kutta scheme, Second Order Equations, Convergence and Consistent

Key concepts: Runge–Kutta methods, Mathematics, Ordinary differential equation, Convergence (economics), Applied mathematics, Order (exchange), Constant (computer programming), Taylor series

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