Need help understanding an Integral method
As a matter of personal interest, I am attempting to program a solver for the method presented in a paper of Tesla-type turbines. The paper is "Integral Method for Flow Between Corotating Disks" and is published by B.E. Boyack and W. Rice through ASME circa 1971.
They develop a system of equations using polynomial expansions of order N. The method they present then generates 2N+2 ODEs, all of which I think I understand. They then state that they use a Runge-Kutta-Gill method to start a Adams-Moulton predictor-corrector method, which I also believe I understand (how the methods work anyway). Where I am running into trouble is mapping the methods onto the equations they formulated.
The equations have unknowns a_i and b_i for i = 0...N and there are some derivatives of these unknowns. In my current understanding, I end up with a complicated to program matrix of these terms, but they are not linearly independent.
My question then would be, is there anyone willing to assist me with an explanation of how these methods map to this problem, or know of a source that discusses this specifically? Maybe there is a more common terminology for it that will assist me in researching it myself that I am not familiar with?
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