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• W2244022897 abstract "The numerical solutions of initial value problems of general second order ordinarydifferential equations have been studied in this work. A new class of continuousimplicit hybrid one step methods capable of solving initial value problems of generalsecond order ordinary differential equations has been developed using the collocationand interpolation technique on the power series approximate solution. The one stepmethod was augmented by the introduction of offstep points in order to circumventDahlquist zero stability barrier and upgrade the order of consistency of the methods.The new class of continuous implicit hybrid one step methods has the advantage ofeasy change of step length and evaluation of functions at offstep points. The Blockmethod used to implement the main method guarantees that each discrete methodobtained from the simultaneous solution of the block has the same order of accuracyas the main method. Hence, the new class of one step methods gives high order ofaccuracy with very low error constants, gives large intervals of absolute stability, arezero stable and converge. Sample examples of linear, nonlinear and stiff problems have been used to test the performance of the methods as well as to compare computedresults and the associated errors with the exact solutions and errors of results obtainedfrom existing methods, respectively, in terms of step number and order of accuracy,using written effcient computer codes." @default.
• W2244022897 created "2016-06-24" @default.
• W2244022897 creator A5024834292 @default.
• W2244022897 date "2011-09-01" @default.
• W2244022897 modified "2023-09-28" @default.
• W2244022897 title "Continuous Implicit Hybrid One-Step Methods for the Solution of Initial Value Problems of General Second-Order Ordinary Differential Equations" @default.
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• W2244022897 hasPublicationYear "2011" @default.
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