Abstract
Block predictor-corrector method for solving non-stiff ordinary differential equations (ODEs) started with Milne’s device. Milne’s device is an extension of the block predictor-corrector method providing further benefits and better results. This study considers Milne’s devise for solving fourth order ODEs. A combination of Newton’s backward difference interpolation polynomial and numerical integration method are applied and integrated at some selected grid points to formulate the block predictor-corrector method. Moreover, Milne’s devise advances the computational efficiency by applying the principal local truncation error (PLTE) of the block predictor-corrector method after establishing the order. The numerical results were exhibited to attest the functioning of Milne’s devise in solving fourth order ODEs. The complete results were obtained with the aid of Mathematica 9 kernel for Microsoft Windows. Numerical results showcase that Milne’s device is more effective than existent methods in terms of design new step size, determining the convergence criteria and maximizing errors at all examined convergence levels.
Highlights
The extension of predictor-corrector method is important for providing some computational benefits to numerical integration of ordinary differential equations
These computational vantages are enlisted in [1, 2]. This composition is primarily concerned with presenting approximate solution of fourth order ordinary differential equations (ODEs) of the form [1,2,3]: y '''' f (x, y, y ', y '', y '''), y(a) 0, y '(a) 1, y ''(a) 2, y '''(a) 3 for ≤ ≤ and : × →
The motivation of this paper is to suggest Milne’s device of variable step-size block predictor-corrector method for solving non-stiff and mildly stiff ODEs implemented in P(EC)m or P(EC)mE mode
Summary
The extension of predictor-corrector method is important for providing some computational benefits to numerical integration of ordinary differential equations. These computational vantages are enlisted in [1, 2]. This composition is primarily concerned with presenting approximate solution of fourth order ODEs of the form [1,2,3]: (1). Scholars have developed straight methods for approximating (1) with better results and efficiency. These methods include block method, block predictor-corrector method, block implicit method, block hybrid method, BDF etc. The backward differentiation formula (BDF) is Gear’s method recognized for www.etasr.com
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