Pointwise convergence of the wavelet solution to the parabolic equation with variable coefficients

We consider the parabolic equation with variable coefficients k(x)uxx = ui, O,x ≤ 1, t ≥ 0, where 0 < a ≤ k(x) < +∞, the solution on the boundary x = O is a given function g and ux(O,t) = O. We use wavelet Galerkin method with Meyer multi-resolution analy-sis to obtain a wavelet approximating solution, and also get an estimate between the exact solution and the wavelet approximating solution of the problem.