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Calculation of integralsg(x)baax iN 1 gxdx ( ) ( ba) gx (i)N i 1 b7Calculation of integralsrandom numbers x i [a,b]homogeneously distributed:„simplesampling“Good if g(x) smooth.8
Error of integrationconventional method:choose N equidistant points distanceone dimensionareahbNwhere T is thecomputer time.error:a1 1N T2h 2 2Δ (N area) 2 T -29Error in d dimensionsin d dimensions:1 1h , T N L d dhTLerror with conventional method:22d 2 2( d1)d Nhh T h Terror with Monte Carlo:1N Monte Carlo better for d > 4T1210
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Adaptive time-stepΔtδ expectedDef
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3th order predictor- correctoruse e
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Comparison of methodsΔtfor fixed n
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