Componentwise partitioning using multistep block method for solving ordinary differential equations

• Published in: Advanced Science Letters
• Main Author: Othman K.I.; Ibrahim Z.B.; Azeany N.A.; Suleiman M.
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84876832360&doi=10.1166%2fasl.2013.4938&partnerID=40&md5=2cc417fb4dcddd4899d782e0d98948ec
• ISSN: 19367317
• DOI: 10.1166/asl.2013.4938

Multistep block method for solving both stiff and non-stiff ordinary differential equations (ODEs) with automatic method selection known as Componentwise Block Partitioning (CBP) is presented. The proposed CBP is a combination of variable step size Block Backward Differentiation Formulas (BBDFs) and block Adams formulas. This solver treats the ODE system as nonstiff initially and solved by Adams method using simple iteration. At the first instance of instability, the appropriate equation which is stiff is placed in the stiff subsystem and solved using BBDF method. An efficiency of the proposed method for solution of ODEs is illustrated on some standard problems found in the literature. © 2013 American Scientific Publishers All rights reserved.