Abstract
A new single-step hybrid block method with three off-step points for the solution of first order ordinary differential equations is proposed. The strategy employed to develop this method is interpolating the power series approximate solution at xn and off-step points and collocating the derivative of the power at xn+1. The class of linear multistep method derived is then simultaneously applied to first order ordinary differential equations together with the associated initial conditions. The numerical results generated are found to be better when compared with the existing methods in terms of error. Besides its excellent performance in term of accuracy, this method also possesses good properties of numerical method such as zero-stable, consistent and convergent.
Highlights
We are interested in finding the numerical solution of first order initial value problems of Ordinary Differential Equations (ODEs) in the following form: y′ = f ( x, y), y ( x0 ) = y0, a ≤ x ≤ b
In overcoming the setbacks mentioned above, Sagir (2014) developed a three-step block method without predictor where three points with a single off-step point were considered as interpolation points for solving first order ordinary differential equations
This paper is divided into four sections; section 1 gives a brief introduction of our work, section 2 explains the derivation of the method, section 3 establishes the properties of the developed block method which include order, error constants, consistency, zerostability and convergence and section 4 presents the numerical results derived when the method was tested on first order initial value problems of ODEs
Summary
We are interested in finding the numerical solution of first order initial value problems of Ordinary Differential Equations (ODEs) in the following form: y′ = f ( x, y), y ( x0 ) = y0, a ≤ x ≤ b (1). Several scholars such as Awoyemi et al (2007), Badmus and Mishelia (2011), Sunday et al (2013) developed numerical methods which were implemented in predictor-corrector mode for solving (1). 00000000e+00 00000000e+00 00000000e+00 00000000e+00 00000000e+00 00000000e+00 1.000000000 e−6 4.800000000 e−5 5.100000000 e−5 6.600000000 e−5
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