Nonlinear integral equation numerical solution
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From: mike3 on 6 Mar 2010 18:37 Hi. Are there methods for obtaining numerical solutions of a nonlinear integral equation like f(x) = int_{-oo...oo} u(x, t, f(t)) dt for f(x)? If so, what would be some good ones?
From: Jon Slaughter on 7 Mar 2010 14:39
mike3 wrote: > Hi. > > Are there methods for obtaining numerical solutions of a nonlinear > integral equation like > > f(x) = int_{-oo...oo} u(x, t, f(t)) dt > > for f(x)? If so, what would be some good ones? I believe the closest you'll get to valid solutions is when u is separable. i.e., u(x,t,f(t)) = f(x)*s(t,f(t))/c with int(s(t,f(t),t=-oo..oo) = c. In any case your integral operator is additive linear in the 3rd argument which allows you to reduce the case to operating on factors that f may contain(such as if f is approximated). This will allow you to search for f by solving the equation on the basis elements. This is much quicker because of the independences it produces. |