Pointwise convergence of the wavelet solution to the parabolic equation with variable coefficients
Jinru Wang, Hua Zhang · Analysis in Theory and Applications · 2008
We consider the parabolic equationwith variable coefficients k ( x ) u xx = u t ,0, x ≤ 1, t ≥ 0, where 0 < α ≤ k ( x ) < +∞, the solution on the boundary x = 0 is a given function g and u x (0 , t ) = 0. We use wavelet Galerkin method with Meyer multi-resolution analysis to obtain a wavelet approximating solution, and also get an estimate between the exact solution and the wavelet approximating solution of the problem.