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- W4385542267 abstract "Abstract In this work, three numerical methods using B-splines have been proposed and numerical solutions of nonlinear time dependent reaction diffusion equations have been obtained. We call the methods as Method I, Method II and Method III. Method I is based on modified cubic B-spline differential quadrature method while Method II and III are based on the colloca-tion of cubic B-spline functions. In Method II, we discretize time derivative by Crank Nicolson scheme and use B-spline functions for spatial derivatives while in Method III , we use modified B-spline functions for spatial variables and derivatives so that it gives a system of ordinary differential equations which is solved by SSP-RK43 method, a method that needs low storage space resulting in less accumulation of computational errors. If we compare three schemes in terms of complexity of implementation, Method I is more straightforward than II and III that evaluates the solution directly rather than computation of time dependent coefficients of B-splines. Considering all aspects involved in the three methods, we conclude that differential quadrature method is better than other two collocation based methods in the numerical experiments carried out." @default.
- W4385542267 created "2023-08-04" @default.
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- W4385542267 date "2023-08-03" @default.
- W4385542267 modified "2023-09-27" @default.
- W4385542267 title "A Study of Cubic B-Spline Based Three Numerical Algorithms for Solving Nonlinear Reaction-diffusion Equations" @default.
- W4385542267 doi "https://doi.org/10.21203/rs.3.rs-3212630/v1" @default.
- W4385542267 hasPublicationYear "2023" @default.
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