| Abstract: | Consider the differential system dy[subscript r]/dx = f[subscript r](x, y₁, y₂, ..., y[subscript m]), y[subscript r](x₀) = r[subscript r0] (r = 1, 2, ..., m). The Runge-Kutte method applies to all functions f[subscript r](x, y₁, y₂, ..., y[subscript m]), of suitable differentiability. By restricting the class of functions to g[subscript r](x) + r[subscript r1]y₁ + ... + c[subscript rm]y[subscript m] where g[subscript r](x) are arbitrary functions of x and c[subscript rj] arbitrary constants, the nth order of this restricted Runge-Kutte method for the explicit case can be defined as [y bar][subscript r1] = y[subscript r0] + [sigma q i=1] R[subscript i]k[subscript ri]. ... |
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