Abstract :
We consider the sideways heat equation uxx(x, t) = ut (x, t), 0 x <1, t 0. The solution u(x, t)
on the boundary x = 1 is a known function g(t). This is an ill-posed problem, since the solution—if
it exists—does not depend continuously on the boundary, i.e., small changes on the boundary may
result in big changes in the solution. In this paper, we shall use the multi-resolution method based
on the Shannon MRA to obtain a well-posed approximating problem and obtain an estimate for the
difference between the exact solution and the solution of the approximating problem defined in Vj .
2004 Elsevier Inc. All rights reserved.
