Advanced Search
All Posts : MaplePrimes Commons General Technical Discussions
Playing with the integral int(cosh(v)/sqrt(sech(v)-sech(vm)),v=0..vm); I have tried numerical integration with different methods and got errors for small vm. Eg. with plain N2:=vm->evalf(Int(cosh(v)/sqrt(sech(v)-sech(vm)),v=0..vm)); N2(.01); returns unevaluated, and with the NAG method N3:=vm->evalf(Int(cosh(v)/sqrt(sech(v)-sech(vm)),v=0..vm,method = _d01ajc)); I get these error messages: N3(.01); Error, (in evalf/int) unable to obtain a real result N3(.001); Error, (in evalf/int) NE_QUAD_ROUNDOFF_TOL: Round-off error prevents the requested tolerance from being achieved: epsabs = 5.0e-013, epsrel = 5.0e-010. Also, the plot plot(N3,0..1); shows holes, presumably for intervals where the algorithm fails to converge to a real result. Curiously, these problems occur where elementary integration is feasible. I wonder the reason of these numerical errors and how to control them. Naively I have increased Digits to 14 and the above plot got much worse!
integration numeric plotting

Please Wait...