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Stochastic Methods for Ill-Posed Problems (2000)

Burrage, K. ; Piskarev, S.

Springer

BIT 40 (2000), S. 226-240

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ISSN: 1572-9125

Keywords: Stochastic differential equations ; regularisation ; stability

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1022386822865

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