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Please use this identifier to cite or link to this item: http://eprint.iitd.ac.in/handle/2074/497

Title: Numerical technique for solving convective-reaction-diffusion equation
Authors: Jain, P C
Shankar, R
Singh, T V
Keywords: Convective-reaction-diffusion equation
Splitting-up technique
Cubic spiines
reactive forces
Issue Date: 1995
Citation: Mathl Comput. Modelling, 22(9), 113-125
Abstract: By using spotting-up technique and cubic splines, a numerical algorithum of second order accuracy is developed to solve the nonlinear equation ut= Re-1 uxx+ [f(U)]x + h(u) with prescribed initial and boundary conditions. The validity of the difference scheme is tested by applying it to the nonlinear Burgers’ equation. The numerical results obtained for Burgers’ equation at low as well as for high Reynolds numbers are found to be in good agreement with the exact solutions. Then, the proposed scheme is used for solving the convective-reaction-diffusion equation ut= Re-1 uxx+ euux + up with initial and boundary conditions. Graphs have been drawn for the numerical solutions at low as well as for high Reynolds numbers by taking the values of parameters in 0 < CI 5 10, 0 < p < 2, and 0 5 E 5 2. The numerical solutions at low values of Re are in steady state for some sets of values of parameters. For intermediate values of Re, the solutions get affected considerably by convective and/or reactive forces, and for high values of Re the solutions blow up. The computed results are compared with the available results for some particular cases.
URI: http://eprint.iitd.ac.in/dspace/handle/2074/497
Appears in Collections:Mathematics

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