A Meshless Method for Solving 1D Heat Equation on a Semicircle

In this work, we present the one-dimensional heat equation solving by the isogeometric method, a meshless method using Galerkin Method. This equation has been solved on a semicircle, a curve on R2. The basis of approximation used for this paper, is the B-splines basis. We define univariate B-splines. We look at their properties as well as b-splines curves. We calculate the numerical solution of the heat equation using the principle of Galerkin’s method. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Solving this partial differential equation leads to solving a system of differential equations. This system will be solved using the classic fourth-order Runge-Kutta method and a CFL condition. Numerical tests have been presented to show the efficiency of this method.