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The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

100%

Lustyk M., Janus J., Pytel-Kudela M., Prykarpatsky A.

Open Mathematics

2009

tom 7

nr 4

775-786

The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated solution sets, based on a Leray-Schauder type fixed point theorem, are obtained.

Richardson Extrapolation combined with the sequential splitting procedure and the θ-method

100%

Zlatev Z., Faragó I., Havasi Á.

Open Mathematics

2012

tom 10

nr 1

159-172

Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.

Ograniczanie wyników

2 Open Mathematics

1 Faragó I.

1 Havasi Á.

1 Janus J.

1 Lustyk M.

1 Prykarpatsky A.

1 Pytel-Kudela M.

1 Zlatev Z.

1 2012

1 2009

Wyniki wyszukiwania

The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

Richardson Extrapolation combined with the sequential splitting procedure and the θ-method