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Topic: A Seven-step Symmetric Linear Multistep Method For Solving Second-order Ordinary Differential Equations.
Description: This work presents a seven-step Symmetric Linear Multistep Method for solving second-order ordinary differential equations. The methodology involves Taylor expansion together with a linear difference operator. The resulting method consists of seven steps and has order eight. The stability, consistency, convergence properties, as well as local truncation error of the constructed method, are presented. The accuracy and efficiency of the method were established by implementing the proposed method on some standard test problems and the results obtained are compared with those discussed in the literature. From the results, our proposed method gave better accuracy compared with those discussed in the literature.
|1.||M.Sc (Mathematics)||Mathematics, Lagos State University Ojo Lagos||2023|
Construction of an Exponentially-Fitted Multiderivative Milne-Simpson Method.
Numerical algorithms for solving the initial value problems whose solution exhibits a pronounced oscillatory behaviour have since the last decade gained a lot of attention. Such problems are often encountered in fields like electronics, astrophysics, mechanics, chemistry, and engineering. Several classical methods methods with only monomials as a basis have been developed by many authors for solving different classes of initial value problems.The application of classical methods to oscillatory problems is significantly hindered because a very small step size is required with a corresponding decrease in performance, especially in terms of efficiency. This work aims to construct a class of two step exponentially-fitted Milne Simpson s methods involving first and second derivatives. This construction is based on the six-step flow chart described in the literature. Here, a classical multi derivative Milne Simpson s method is constructed and fitted exponentially to allow for easy application to oscillatory or periodic problems. This work extends the classical two-step fourth-order Milne-Simpson s method to involve the second derivative and hence increasing the attainable order of the method, the extended method is also fitted exponentially. The constructed class of methods is shown to be of the order of six 6 and well-suited for oscillatory problems.
KAZEEM MOSHOOD is a Graduate Assistant at the Department of Mathematics
KAZEEM has a M.Sc in Mathematics from Mathematics, Lagos State University Ojo Lagos