One Phase Moving Boundary Problem
P. Kanakadurga Devi1, V. G. Naidu2

1P. Kanakadurga Devi*, Department of Mathematics, MLR Institute of Technology, Hyderabad, India.
2V. G. Naidu, Adama Science and Technology University,  Ethiopia.
Manuscript received on November 22, 2019. | Revised Manuscript received on December 15, 2019. | Manuscript published on December 30, 2019. | PP: 3427-3431 | Volume-9 Issue-2, December, 2019. | Retrieval Number:  E7501068519/2019©BEIESP | DOI: 10.35940/ijeat.E7501.129219
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Abstract: In this paper we introduced a variable time step method to obtain interface to moving boundary problem for Slab and Sphere. We present the basic difficulty, apart from the need to find the moving boundary, that there is no domain for the space variable. This difficulty is handled by the age old principles of basic mathematics. Naturally, giving symbolic names to the unknowns develop equations involving them and solve it using the conditions of the problem. High order accurate initial time step sizes for given space step size are obtained with the help of Green’s theorem. The Subsequent time steps are obtained by an iterative scheme. This variable time step method handles Dirichlet’s problem of freezing or melting of a Slab and spherical droplet.
Keywords: Interface, Finite difference method, Crank-Nicolson scheme, Stefan problem, Variable time step.