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A Class of P-Stable Hybrid Linear Multistep Methods with Minimal Phase-Lag Error for Second Order Initial Value Problems



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Master's Thesis from the year 2018 in the subject Mathematics - Miscellaneous, grade: 82.0%, University of Benin, language: English, abstract: P-stable hybrid linear multistep methods (HLMMs) have been an interesting focus for the numerical solution of second order initial value problems (IVPs) in ordinary di_erential equations (ODEs), because of their high order of accuracy. In this thesis, we present a new class of P-stable HLMMs with order p = 2 and p = 4 respectively for the numerical solution of second order systems. The hybrid schemes which are obtained via Pade 0 approximation approach have minimum Phase-lag error. Numerical experiments are carried out to show the accuracy of the proposed schemes. Nevertheless, the desire in this work is on high order P-stable schemes (p > 4). We give a proposition with proof, stating the limitation of the approach in search for higher order P-stable formulas. Key words: P-stability, Phase-lag error (PLE) constant, Hybrids, order, Interval of periodicity, Pade 0 approximation, Principal local truncation error (PLTE).






Master's Thesis from the year 2018 in the subject Mathematics - Miscellaneous, grade: 82.0%, University of Benin, language: English, abstract: P-stable hybrid linear multistep methods (HLMMs) have been an interesting focus for the numerical solution of second order initial value problems (IVPs) in ordinary di_erential equations (ODEs), because of their high order of accuracy. In this thesis, we present a new class of P-stable HLMMs with order p = 2 and p = 4 respectively for the numerical solution of second order systems. The hybrid schemes which are obtained via Pade 0 approximation approach have minimum Phase-lag error. Numerical experiments are carried out to show the accuracy of the proposed schemes. Nevertheless, the desire in this work is on high order P-stable schemes (p > 4). We give a proposition with proof, stating the limitation of the approach in search for higher order P-stable formulas. Key words: P-stability, Phase-lag error (PLE) constant, Hybrids, order, Interval of periodicity, Pade 0 approximation, Principal local truncation error (PLTE).


Several symmetric hybrid two step sixthorder Pstable methods for the numerical integration of second order periodic initial value problems have been considered in this paper. Multistep phasefitted methods and multistep methods with minimal phaselag . Franco A class of explicit twostep hybrid methods for 21 T. High order pstable formulae for the numerical integration of periodic initial value problems.


Order P

Kirjailija . The second chapter deals with RungeKutta and extrapolation methods not only for the standard firstorder problem but also for various extensions thereof such as secondorder and delay equations. Abstract Enumath 2013. 0 no final method is needed and becomes an initial value method IVM that is a classical multistep method with only initial conditions.It Stability.While attempting to seek generalizations of the linear stability theory to nonlinear problems a great deal of interest was devoted to the class of. A class of pstable linear multistep numerical methods. We adopted method of interpolation and collocation of power series approximate solution to generate the continuous hybrid linear multistep method which was evaluated at grid points to give a contnuous block method. A Class of PStable Hybrid Linear Multistep Methods with Minimal PhaseLag Error for Second Order Initial Value Problems. The phaselag analysis of the method 1.2 1.3 is investigated using the homogeneous test equation y 2 i y t. Numerische Mathema. Pstable or of large interval of periodicity and of high phaselag error order . Multistep phase fitted methods with minimal phaselag are obtained in 1 2 3 4.


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