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A family of r-points 1-block implicit methods with optimized region of stability for stiff initial value problems in ordinary differential equations
International Journal of Statistics and Applied Mathematics · 2022 · Vol. 7(4) · pp. 22–35
I. M. Esuabana✉(University of Uyo)SE EkoroFA Adie(University of Calabar)U. A. Abasiekwere(University of Uyo)
Abstract
In this paper, we proposed a family of r-points 1-block implicit methods with optimized region of stability. This family of methods is derived with Mathematical 10.4 software and the stability is investigated using boundary locus techniques. The block methods are consistence, zero stable, and A-stable and satisfy other stability requirements which finds them suitable for stiff problems in ODEs. Numerical experiments are presented and results are compared with other block methods and exact solutions of some stiff ordinary differential equations. The methods have been found to show competitiveness with other numerical methods.
Numerical methods for differential equationsMatrix Theory and AlgorithmsDifferential Equations and Numerical MethodsMathematicsOrdinary differential equationBlock (permutation group theory)Stability (learning theory)L-stabilityOdeBoundary value problemStiff equationApplied mathematicsNumerical methods for ordinary differential equations
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