Numerical Simulation of one dimensional Heat Equation: B-Spline Finite Element Method

The comprehensive numerical study has been made here for the solution of One dimensional heat equation the Finite Element method is adopted for the solution with B-spline basis function the important finding of the present study is to understand the basics behind the FEM method while the B-spline basis function come into the picture here the solution is made using Quadratic B-spline and Cubic B-spline. Then for both the cases the solution is compare with analytical solution in which a good agreement is found between proposed technique. Along with that the simulation process is made using MATLAB programming in which the 3-Dimensional geometrical intrepitaion shown as a graphical presentation taken a different time steps as well as different domain of interest , the dirichlet boundary condition has been taken for the solution of this problem which is again a good achievement of the above work along with two test problem has been taken for the sake of convince. Finally the goal has been achieved in a simulation process. Keywords; Quadratic B-spline, Cubic B-spline, FEM, Stability, Simulation, MATLAB