International Journal of Numerical Methods and Applications
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Abstract: We consider the nonhomogeneous problem where the Cauchy data is given at
This is an
ill-posed problem in the sense that a small disturbance on the boundary can produce
a big alteration in its solution (if it exists). In this paper, we define a
Meyer wavelet solution to obtain the well-posed solution in the scaling space We also
show that under certain conditions, this regularized solution is convergent to
the exact solution. In the previous papers, most of the theoretical results
concerning the error estimate were about the homogeneous equation, i.e.,
