ADAPTIVE FUP COLLOCATION METHOD FOR TIME DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

We present an adaptive method for numerical solving boundary-initial value problems. To solve ID initial boundary value problem, we convert the problem into 2D problem. This boundary value problem is then solved by using infinitely differentiable basis functions with compact support called Fup basis functions and the collocation technique. Partial differential equations are solved simultaneously in the space-time domain with resolved all space and time multiple scales. The proposed method is generally meshless method because it requires only adding of collocation points and basis functions over the domain, not the classic domain discretization and the numerical integration. Numerical adaptive algorithm adds new collocation points in the next resolution level only in the space-time zones where solution correction is greater than the prescribed threshold. With this approach, the Fup coefficients measure the local fluctuation of the solution simultaneously in space and time.