New efficient time integrators for non-linear parabolic problems

• Autorzy: Bujanda B. , Jorge J. C.
• Języki publikacji: EN

Abstrakty

EN

In this work a new numerical method is constructed for time-integrating multidimensional parabolic semilinear problems in a very efficient way. The method reaches the fourth order in time and it can be combined with standard spatial discretizations of any order to obtain unconditionally convergent numerical algorithms. The main theoretical results which guarantee this property are explained here, as well as the method characteristics which guarantee a very strong reduction of computational cost in comparison with classical discretization methods.

Słowa kluczowe

EN

fractional step methods; non-linear parabolic problems; convergence

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 3
• Strony: 407--419
• Opis fizyczny: Bibliogr. 8 poz., tab.

Twórcy

autor

Bujanda B.

autor

Jorge J. C.

• Universidad Pública de Navarra, Dpto. Mathemática e Informática,

Bibliografia

• [1] B. Bujanda, J.C. Jorge, Stability results for linearly implicit Fractional Step discretizations of non-linear time dependent parabolic problems, to appears in Appl. Num. Math.
• [2] B. Bujanda, J.C. Jorge, Order conditions for linearly implicit Fractional Step Runge-Kutta methods (Preprint), Universidad Publica de Navarra.
• [3] B. Bujanda, J.C. Jorge, Efficient linearly implicit methods for nonlinear multidimensional parabolic problems, 3. Comput. Appl. Math. 164/165 (2004), 159-174.
• [4] B. Bujanda, J.C. Jorge, Stability results for fractional step discretizations of time dependent coefficient evolutionary problems, Appl. Numer. Math. 38, (2001), 69-86.
• [5] G.J. Cooper, A. Sayfy, Aditive methods for the numerical solution of ordinary differential equations, Math. of Comp. 35, (1980), 1159-1172.
• [6] E. Hairer, G. Wanner, Solving ordinary differential equations II, Springer-Verlag, 1987.
• [7] W. Hundsdorfer, J.G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer, 2003.
• [8] N.N. Yanenko, The method of fractional steps, Springer, 1971.