High order block method for third order ODEs

Asnor, A.I. and Yatim, S.A.M. and Ibrahim, Z.B. and Zainuddin, N. (2021) High order block method for third order ODEs. Computers, Materials and Continua, 67 (1). pp. 1253-1267.

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Abstract

Many initial value problems are difficult to be solved using ordinary, explicit step-by-step methods because most of these problems are considered stiff. Certain implicit methods, however, are capable of solving stiff ordinary differential equations (ODEs) usually found in most applied problems. This study aims to develop a new numerical method, namely the high order variable step variable order block backward differentiation formula (VSVO-HOBBDF) for the main purpose of approximating the solutions of third order ODEs. The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code. The order of the proposed method was then discussed in detail. The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively. In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB, particularly ode15s and ode23s, a numerical experiment was conducted on a set of stiff problems. The numerical results prove that for this particular set of problem, the use of the proposed method is more efficient than the comparable methods. VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs. Â© 2021 Tech Science Press. All rights reserved.

Item Type: Article cited By 0 Efficiency; Initial value problems; Ordinary differential equations, Approximate solution; Backward differentiation formulae; Computational work; Numerical experiments; Numerical results; Step-by-step method; Stiff ordinary differential equations; Third-order odes, Numerical methods 23854 Ms Sharifah Fahimah Saiyed Yeop 19 Aug 2021 13:08 19 Aug 2021 13:08

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