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Multigrid method for numerical solution of ordinary differential equations

100%

Kozakiewicz J. M., Mika J. R.

Mathematica Applicanda

1992

tom 21

nr 35

We consider the initial value problem for systems of ordinary differential equations such that the solution vector can be split into subvectors and each subvector represented as a product of a scalar amplitude and a shape vector which changes slowly with time. The equations for the shape vectors can be solved with much larger time steps than those required for the original equations. The numerical results show that a substantial reduction in the computing time may be achieved

Determining the step of integration for the one-step Bobkov's methods

63%

Szyszkowicz M.

Mathematica Applicanda

1985

tom 13

nr 25

Consider the class of Bobkov methods for solving the IVP: y′=f(x,y), x[a,b]. Four procedures for finding the step size h are presented. It is shown that these Bobkov methods with automatic stepsize control are faster (i.e. need fewer evaluations of f) than the corresponding Runge-Kutta methods.

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

44%

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 Mathematica Applicanda

1 Open Mathematics

1 Faragó I.

1 Havasi Á.

1 Kozakiewicz J. M.

1 Mika J. R.

1 Szyszkowicz M.

1 Zlatev Z.

1 2012

1 1992

1 1985

Wyniki wyszukiwania

Multigrid method for numerical solution of ordinary differential equations

Determining the step of integration for the one-step Bobkov's methods

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