A Quarter-Step Hybrid Block Method for First-Order Ordinary Differential Equations

Three-step optimized block backward differentiation formulae (TOBBDF) for solving stiff ordinary differential equations

“…A stiffequation is a differential equation that is characterized as that whose exactsolution has a term of the form, cx e  where c is a large positive constant (Sunday et al, 2015).…”

“…Consider the mildly stiff initial value problem (Raymond et al, 2018;Yakusat et al, 2015): Consider the first-order stiff initial value problem (Sunday et al, 2015): Table 2, the comparison of error in problem 3 were made. The results perform better than Raymond (2018), which has order 8 against our method of order 6.…”

“…Several numerical problems will be solved and comparison will be made with other methods to show the efficiency of the proposed method (Table 1). This paper considers an approximate method for the solutionof stiff differential equation of first-order initial value problem of the form, wheref (x, y) iscontinuousandsatisfiesthe existenceand uniquenesstheorem (Henrici, 1962).Recently many authors have applied hybrid block method with adifferent number of steps and hybrid points to find numerical solutionsfor the first-order differential equations (Sagir, 2014;Raymond et al, 2018;Ramos, 2017;Areo and Adeniyi, 2014;Yakusak and Adeniyi, 2015;Yahaya and Tijjani, 2015;Fotta and Alabi, 2015;Sunday et al, 2015). In this paper, we optimizedthe local truncation errors to find three off-points in one stepto obtain the most accurate solution.…”

“…The algorithm presented in this paper is based on block method and approximates the solution at several points (Raymond et al, 2018;Olanegan et al, 2015;Areo and Adeniyi, 2014;Yakusak and Adeniyi, 2015). Block methods were first introduced by Yahaya and Tijjani (2015) as a means of obtaining starting values for predictor-corrector algorithms and has since then been developed by several researchers (Milne, 1953;Fotta and Alabi, 2015;Sunday et al, 2015;Odejide and Adeniran, 2012), for general use. This paper presents a block method which preserves the Runge-Kutta traditional advantage of being self-starting and efficient.…”

An Accurate Implicit Quarter Step First Derivative Block Hybrid Method (AIQSFDBHM) for Solving Ordinary Differential Equations

“…Over the years, several researchers have considered the important numerical solution of (1.1). Sunday et al [3] developed a quarter-step hybrid block method for solving (1.1), [4] constructed an A-stable uniform order six linear multi-step methods for direct integration of (1.1). Also, Skwame et al [5] construct an implicit one-step block hybrid methods with multiple off-grid points for solving (1.1).…”