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Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation

100%

Koley U.

Open Mathematics

2012

tom 10

nr 1

173-187

We are concerned with convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (Kawahara equation, in short), which is a transport equation perturbed by dispersive terms of the 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the standard Fourier-Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L 2-error bound of spectral accuracy in space and of second-order accuracy in time.

Numerical schemes for multivalued backward stochastic differential systems

88%

Maticiuc L., Rotenstein E.

Open Mathematics

2012

tom 10

nr 2

693-702

We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: $$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$ where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational inequality in conjunction with Yosida approximation techniques.

Ograniczanie wyników

2 Open Mathematics

1 Koley U.

1 Maticiuc L.

1 Rotenstein E.

2 2012

Wyniki wyszukiwania

Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation

Numerical schemes for multivalued backward stochastic differential systems