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Home  >  Volume 46 (May, 2018)

5. GENERALIZED ADAMS-TYPE THIRD DERIVATIVE METHODS FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS by G. C. Nwachukwu and N. E. Mokwunyei Volume 46 May, 2018, pp35 –44
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GENERALIZED ADAMS-TYPE THIRD DERIVATIVE METHODS FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS

G. C. Nwachukwu and N. E. Mokwunyei

Advanced Research Laboratory

Department of Mathematics, University of Benin, Benin City, Nigeria. 

Abstract

The objective of this study is to construct a family of third derivative generalized Adams-type methods (TDGAMs) for the solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs) by means of boundary value methods (BVMs) approach. Some numerical properties such as stability of the methods are investigated and the methods are shown to be 0_(v,k-v)-stable and A_(v,k-v)-stable with (v,k-v)-boundary conditions for all values of the step length k≥1 . These methods have high order up to  p=3k+3 and small error constants. Some experimental problems reveal that the methods are suitable for the solution of stiff initial value problems.

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