A Numerical Method Based Boundary Integral Equation to Solve Multiphase Moving Boundary Problems
S. G. Ahmed *
Department of Engineering Mathematics and Numerical Analysis, Faculty of Engineering, Zagazig University, Zagazig, P.O.Box 44519, Egypt.
M. Saif AlDien
Department of Mathematics, Taif University, Taif-Al-Haweiah, P.O.Box 888, Zip Code 21974, Kingdom of Saudi Arabia.
M. Y. Youssef
Department of Mathematics, Taif University, Taif-Al-Haweiah, P.O.Box 888, Zip Code 21974, Kingdom of Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
The present paper deals with moving boundary problems by fixing the moving boundary by an assumption of the form 
is assumed power and ς is an unknown. An iterative algorithm is then developed within the main algorithm to solve the phases that appear throughout the m whole process with moving boundaries at each time step as phases with fixed boundaries. A two test problems are solved using the present method. The results due to the first test problem were compared with previous numerical results based on boundary integral formulation, while the results due to the second one was compared with available analytical solution. An overall good agreement is obtained for both two examples compared with the previous numerical and analytical results.
Keywords: Phase change problems, moving boundary problems, boundary elements methods, numerical algorithms