FINITE-DIFFERENCE METHODS FOR 12TH-ORDER BOUNDARY-VALUE-PROBLEMS

[摘要] The effect of rotation acting on a layer of fluid heated from below is similar to the effect of a magnetic field acting under the same conditions: they both inhibit the onset of instability and they both elongate the cells which appear at marginal stability. However, it must not be assumed that, acting together, rotation and magnetic field reinforce each other. In fact, they have conflicting tendencies when acting together. The effect of rotation and magnetic field together leads to a twelfth-order eigenvalue problem (Chandrasekhar (1961)) which will be addressed in a future paper. Experience in solving high-order boundary-value problems has shown that considerable insight may be obtained by solving the special problem first. Moreover, beside the mathematical interest, the computational aspects of the special problem need to be considered. To this end, finite-difference methods of order two and global extrapolation on two grids are proposed to solve the following special nonlinear twelfth-order boundary-value problem: w(xii)(x) = f(x, w), a < x < b, w(2i)(a) = A2i, w(2i)(b) = B2i, i = 0, 1,...,5. A simple example is carried out to illustrate the results given by the methods.

[发布日期] 1991-06-26

[效力级别]  Proceedings Paper

[关键词] 12TH-ORDER BOUNDARY-VALUE PROBLEMS;FINITE-DIFFERENCE METHODS;SPECIAL PROBLEM;GLOBAL EXTRAPOLATION