Abstract
This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = \(\sqrt {\tau _n }\), where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.
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Burrage, K., Piskarev, S. Stochastic Methods for Ill-Posed Problems. BIT Numerical Mathematics 40, 226–240 (2000). https://doi.org/10.1023/A:1022386822865
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DOI: https://doi.org/10.1023/A:1022386822865