Galpern—Sobolev Type Equations with Non-constant Coefficients
We study Galpern—Sobolev equations by the help of a quaternionic operator calculus. Some previous work will be extended to the case of variable coefficients. Rothe’s time discretization method is used to reduce the problem to a series of stationary problems. Solving the resulting stationary problems by means of quaternionic analysis we obtain integral representation formulas for the solution of the Galpern-Sobolev equation. The truncation error and the stability of the method is studied, too.
KeywordsGalpern—Sobolev equations representation formulas operator calculus finite difference schemes
Mathematics Subject Classification (2000)Primary: 30G35 Secondary 35G15
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