Transcription of Richardson Extrapolation
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Richardson ExtrapolationThere are many approximation procedures in which one first picks a step sizehandthen generates an approximationA(h) to some desired quantityA. Often the order of theerror generated by the procedure is known. In other wordsA=A(h) +Khk+K hk+1+K hk+2+ withkbeing some known constant andK, K , K , being some other (usually unknown)constants. For example,Amight be the valuey(tf) at some final timetffor the solution toan initial value problemy =f(t, y), y(t0) =y0. ThenA(h) might be the approximationtoy(tf) produced by Euler s method with step sizeh. In this casek= 1. If the improvedEuler s method is usedk= 2.
Richardson Extrapolation There are many approximation procedures in which one first picks a step size hand then generates an approximation A(h) to some desired quantity A.
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