Formulation of Variable Step Block Backward Differentiation Formula for the Computation of Nonlinear Fuzzy Differential Equations
DOI:
https://doi.org/10.62054/ijdm/0104.04Keywords:
Backward differentiation formula, Nonlinear fuzzy differential equations, Variable stepsize, UncertaintyAbstract
The research paper formulates a variable step block backward differentiation formula (VSBBDF) for solving nonlinear fuzzy differential equations (FDEs). Developed to address uncertainties within differential equations by using fuzzy environments, VSBBDF offers a flexible approach to solve equations with triangular fuzzy numbers. This method incorporates a dynamic step-size selection, allowing it to adapt to changes and reduce computational costs while maintaining accuracy. The paper further discusses the stability and convergence properties of VSBBDF, demonstrating that it is both zero-stable and of high accuracy. The results obtained highlight the method's computational efficiency and reliability, particularly when compared with other existing methods for solving nonlinear FDEs.
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Sekar, S. and Sakthivel, A. (2015), Numerical investigation of linear first order fuzzy differential equations using He’s homotopy perturbation method, IOSR Journal of Mathematics, Vol. 11, No. 5, pp.33-38.
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Zadeh, L.A. (1965), Fuzzy sets, Information and Control, Vol. 8, No. 8, pp.338-353, DOI:10.1016/S0019-9958(65)90241-X.
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