On the Chebyshev method to linear parabolic P.D.E.s with inhomogeneous mixed boundary conditions. (English) Zbl 0602.65088

Doha, E. H.

Arab J. Math. 4, 29-57 (1983).

This paper discusses a numerical method for obtaining an approximate solution of the parabolic equation \(p(x,t)\partial u/\partial t=\partial^ 2u/\partial x^ 2\) subject to inhomogeneous mixed boundary conditions, by expanding u as Chebyshev series in the x-direction, and obtaining a set of ordinary differential equations in the time direction for the coefficients of the expansion. The method is an extension of that of P. Dew and R. Scraton [J. Inst. Math. Appl. 9, 299-309 (1972; Zbl 0237.65072)]. The extension of the method to polar-type equations of the form \(p(x,t)\partial u/\partial t=\partial^ 2u/\partial x^ 2+(1/x)(\partial u/\partial x)\) is also described.

MSC:

65N40	Method of lines for boundary value problems involving PDEs
35K20	Initial-boundary value problems for second-order parabolic equations

Keywords:

Chebyshev method; Chebyshev series; polar-type equations