Introduction: Many problems in science and engineering can be formulated as ordinary differential... more Introduction: Many problems in science and engineering can be formulated as ordinary differential equations. The analytical methods of solving differential equations are applicable only to a selected class of differential equations. Quite often, equations appearing in physical problems do not belong to any of these familiar types and one is obliged to resort to numerical methods for solving such differential equations. Linear multistep methods are very popular for solving first order initial value problems. Aims: In this paper, the optimal 8-step linear multistep method for solving y ′ = f (x, y) is constructed and implemented. Materials and Methods: The construction was carried out using the technique based on the Taylor expansion of y(x + jh) and y ′ (x + jh) about x + th, where t need not necessarily be an integer. Results: The consistency, stability and convergence of the proposed method are investigated. To investigate the accuracy of the method, a comparison with the classical 8-stage Runge-Kutta method is carried out on two numerical examples. Conclusion: In this work, the procedure for the construction of an optimal 8-step linear multistep method for first-order differential equations has been presented. The constructed method is consistent and zero-stable. Hence it is convergent. The accuracy of the method compared with the well-known Runge-Kutta method is demonstrated by its application to two test problems.
In recent times, the derivation of Runge-Kutta methods based on averages other than the arithmeti... more In recent times, the derivation of Runge-Kutta methods based on averages other than the arithmetic mean is on the rise. In this paper, the authors propose a new version of explicit Runge-Kutta method, by introducing the harmonic mean as against the usual arithmetic averages in standard Runge-Kutta schemes.
Journal of Informatics and Mathematical Sciences, 2020
In this paper, two different classes of mappings namely, uniformly continuous asymptotically none... more In this paper, two different classes of mappings namely, uniformly continuous asymptotically nonexpansive and uniformly continuous asymptotically demicontractive mappings are considered on the general modified Noor iteration process with errors and proved to converge strongly to the fixed point of uniformly continuous asymptotically demicontractive mappings in uniformly smooth Banach spaces. The new result can be viewed as an improvement to a multitude of results in the fixed point theory especially those of Xu and Noor [8], Owojori and Imoru [5] and also the results of Owojori [6].
In this paper, the authors show that the general linear second order ordinary Differential Equati... more In this paper, the authors show that the general linear second order ordinary Differential Equation can be formulated as an optimization problem and that evolutionary algorithms for solving optimization problems can also be adapted for solving the formulated problem. The authors propose a polynomial based scheme for achieving the above objectives. The coefficients of the proposed scheme are approximated by an evolutionary algorithm known as Differential Evolution (DE). Numerical examples with good results show the accuracy of the proposed method compared with some existing methods.
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Papers by Bakre Fatimah