Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative | Zendy

Richard M. Beam | Zendy; R. F. Warming | Zendy

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Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative

Author(s) -

Richard M. Beam,

R. F. Warming

Publication year - 1980

Publication title -

siam journal on scientific and statistical computing

Language(s) - English

Resource type - Journals

eISSN - 2168-3417

pISSN - 0196-5204

DOI - 10.1137/0901007

Subject(s) - alternating direction implicit method , mathematics , derivative (finance) , factorization , second derivative , parabolic partial differential equation , mathematical analysis , linear multistep method , time derivative , space (punctuation) , numerical analysis , partial differential equation , finite difference method , differential equation , algorithm , computer science , differential algebraic equation , ordinary differential equation , financial economics , economics , operating system

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all $A_0 $-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit $A_0 $-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

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