Solving Integral Equations

08242019, 09:07 PM
(This post was last modified: 09072019 08:00 PM by Albert Chan.)
Post: #2




RE: Solving Integral Equations
Hi, Eddie
My guess is the integral calculations will take the most time. Instead of always do integral from 0 to x, why not reuse old integral calculations ? ∫(f(u), u=0 to x) = ∫(f(u), u=0 to t) + ∫(f(u), u=t to x) (08242019 03:34 PM)Eddie W. Shore Wrote: ∫( sin^2 t dt, 0, x) = 1.4897 This is my Mathematica code, only for proof of concept. Quote:f[x_] := Sin[x]^2; > NestList[newton, 1.0, 5] {1.0, {2.71878, 1., 0.272676}, {2.38150, 2.71878, 1.54649}, {2.48529, 2.38150, 1.44043}, {2.49964, 2.48529, 1.48436}, {2.49991, 2.49964, 1.4896}} Note: x=2.49991 already converged to 1.4897. The value 1.4896 were previous integral, 0 to 2.49964 

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Solving Integral Equations  Eddie W. Shore  08242019, 03:34 PM
RE: Solving Integral Equations  Albert Chan  08242019 09:07 PM

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