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2015•Unpublished venueRequires access

Reformulation of Block Implicit Linear Multistep Method into Runge Kutta Type Method for Initial Value Problem

Raihanatu Muhammad, Y. A. Yahaya

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Abstract

In this research work, we reformulated the block hybrid Backward Differentiation Formula (BDF) for ��= 4 into Runge Kutta Type Method (RKTM) of the same step number for the solution of Initial value problem in Ordinary Differential Equation (ODE). The method can be use to solve both first and second order (special or general form). It can also be extended to solve higher order ODE. This method differs from conventional BDF as derivation is done only once.

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What this paper is about

In this research work, we reformulated the block hybrid Backward Differentiation Formula (BDF) for ��= 4 into Runge Kutta Type Method (RKTM) of the same step number for the solution of Initial value problem in Ordinary Differential Equation (ODE). The method can be use to solve both first and second order (special or general form). It can also be extended to solve higher order ODE. This method differs from conventional BDF as derivation is done only once.

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Available abstract

In this research work, we reformulated the block hybrid Backward Differentiation Formula (BDF) for ��= 4 into Runge Kutta Type Method (RKTM) of the same step number for the solution of Initial value problem in Ordinary Differential Equation (ODE). The method can be use to solve both first and second order (special or general form). It can also be extended to solve higher order ODE. This method differs from conventional BDF as derivation is done only once.

Key concepts: Ode, Runge–Kutta methods, Linear multistep method, Mathematics, Backward differentiation formula, Ordinary differential equation, Initial value problem, Block (permutation group theory)

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