Search results for: BDF
4 Development Partitioning Intervalwise Block Method for Solving Ordinary Differential Equations
Authors: K.H.Khairul Anuar, K.I.Othman, F.Ishak, Z.B.Ibrahim, Z.Majid
Abstract:
Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of computational effort. Therefore, PBI is developed in order to reduce the cost of iteration within acceptable maximum errorKeywords: Adam Block Method, BDF, Ordinary Differential Equations, Partitioning Block Intervalwise
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17083 An eighth order Backward Differentiation Formula with Continuous Coefficients for Stiff Ordinary Differential Equations
Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa
Abstract:
A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28162 Parallel Block Backward Differentiation Formulas for Solving Ordinary Differential Equations
Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman
Abstract:
A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20641 Fifth Order Variable Step Block Backward Differentiation Formulae for Solving Stiff ODEs
Authors: S.A.M. Yatim, Z.B. Ibrahim, K.I. Othman, F. Ismail
Abstract:
The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precision and computation time. The strategy involves constant, halving or increasing the step size by 1.9 times the previous step size. Decision of changing the step size is determined by the local truncation error (LTE). Numerical results are provided to support the enhancement of method applied.Keywords: Backward differentiation formulae, block backwarddifferentiation formulae, stiff ordinary differential equation, variablestep size.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2305