Abstract
The seriously ill-posed sideways heat equations were considered in the quarter plane. The classical quasi-reversibility method was applied to acquire an approximate but non-regularized solution to the problem. Interestingly, a regularization solution to the sideways heat equation was obtained through modification of the denominator of the solution. Then, a new regularization method was proposed, and the Hlder-type error estimates under a priori and a posteriori parameter choice rules were proved, respectively. Numerical experiments show the feasibility and effectiveness of the proposed method.
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