# MULTI-BLOCK BOUNDARY VALUE METHODS FOR ORDINARY DIFFERENTIAL AND DIFFERENTIAL ALGEBRAIC EQUATIONS

• OGUNFEYITIMI, S.E. (ADVANCED RESEARCH LABORATORY, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF BENIN) ;
• IKHILE, M.N.O. (ADVANCED RESEARCH LABORATORY, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF BENIN)
• Accepted : 2020.08.25
• Published : 2020.09.25

#### Abstract

In this paper, multi-block generalized backward differentiation methods for numerical solutions of ordinary differential and differential algebraic equations are introduced. This class of linear multi-block methods is implemented as multi-block boundary value methods (MB2 VMs). The root distribution of the stability polynomial of the new class of methods are determined using the Wiener-Hopf factorization of a matrix polynomial for the purpose of their correct implementation. Numerical tests, showing the potential of such methods for output of multi-block of solutions of the ordinary differential equations in the new approach are also reported herein. The methods which output multi-block of solutions of the ordinary differential equations on application, are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output only a block of solutions per step. The MB2 VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.

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