zbMATH — the first resource for mathematics

An application of quaternionic analysis to the solution of time- independent Maxwell equations and of Stokes equation. (English) Zbl 0704.35128
Abstract analysis, Proc. 14th Winter Sch., Srní/Czech. 1986, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 14, 61-76 (1987).
[For the entire collection see Zbl 0627.00012.]
Special 3-dimensional boundary value problems (with smooth boundaries) can be solved in an effective manner by relating the boundary collocation method, as a synthesis of analytical and numerical techniques, with an operator calculus based on so called quaternionic analysis, where quaternions are special four-dimensional vectors. So, suitable operators are described and included in a general operator theory. Then, the boundary collocation method is presented and applied to find an approximative solution of time-independent Maxwell equations, with constant or x-dependent parameters, respectively to Stokes’ equation. To appropriate the paper, most of the mentioned literature should be consulted.
Reviewer: J.Appeltauer
35Q60 PDEs in connection with optics and electromagnetic theory
35Q35 PDEs in connection with fluid mechanics
65Z05 Applications to the sciences
35L50 Initial-boundary value problems for first-order hyperbolic systems
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
Zbl 0627.00012