Hi;
I have a complex numerical integration and i get the following error : "Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.1e+138. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy."
My Matlab codes as
function trns2 clcglobal kpp;global teta;global eta;%**************************************************************
%********************P A R A M E T E R S***********************
%**************************************************************lmd=1.55e-6; %wavelength
%L=50; %distance
k=2*pi/lmd;%******************oceanic parameters**********************
eta_s=1e-3; %kolmogorov microscale length
x_t=1e-6; %rate of dissipation of mean-squared temperature
eps=1e-4; %rate of dissipation of kinetic energy per unit mass of fluid
%w=-1; %ratio of temperature to salinity contributions to the refractive index spectrum
A_t=1.863e-2;A_s=1.9e-4;A_ts=9.41e-3;%***************************************************************
%***************************************************************%***************************************************************p1x=0.02;p1y=0;p2x=0.02;p2y=0;w1=-1;w2=-2;w3=-5;coeff1=0.388*pi*(1e-8)*k*k*(eps^(-1/3))*x_t/(w1*w1);coeff2=0.388*pi*(1e-8)*k*k*(eps^(-1/3))*x_t/(w2*w2);coeff3=0.388*pi*(1e-8)*k*k*(eps^(-1/3))*x_t/(w3*w3);j=1;for L=10:10:50f1=@(eta,kpp,teta)((kpp.^(-8/3)).*(1+2.35*((kpp*eta_s).^(2/3))).*... (w1*w1*exp(-A_t*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))+exp(-A_s*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))-2*w1*exp(-A_ts*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))).*... ((exp(1i*k*(p1x*p1x+p1y*p1y-p2x*p2x-p2y*p2y)./(L-eta)).*exp(1i*kpp.*cos(teta)*(p1x-p2x)).*exp(1i*kpp.*sin(teta)*(p1y-p2y)))-(exp(1i*k*(p1x*p1x+p2x*p2x+p1y*p1y+p2y*p2y)./(L-eta)).*exp(1i*kpp.*cos(teta)*(p1x-p2x)).*exp(1i*kpp.*sin(teta)*(p1y-p2y)).*exp(1i*(eta-L).*kpp.*kpp/k))));Bx1=integral3(f1,0,L,0,inf,0,2*pi);BxR1(j)=coeff1*(real(Bx1))f2=@(eta,kpp,teta)((kpp.^(-8/3)).*(1+2.35*((kpp*eta_s).^(2/3))).*... (w2*w2*exp(-A_t*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))+exp(-A_s*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))-2*w2*exp(-A_ts*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))).*... ((exp(1i*k*(p1x*p1x+p1y*p1y-p2x*p2x-p2y*p2y)./(L-eta)).*exp(1i*kpp.*cos(teta)*(p1x-p2x)).*exp(1i*kpp.*sin(teta)*(p1y-p2y)))-(exp(1i*k*(p1x*p1x+p2x*p2x+p1y*p1y+p2y*p2y)./(L-eta)).*exp(1i*kpp.*cos(teta)*(p1x-p2x)).*exp(1i*kpp.*sin(teta)*(p1y-p2y)).*exp(1i*(eta-L).*kpp.*kpp/k))));Bx2=integral3(f2,0,L,0,inf,0,2*pi);BxR2(j)=coeff2*(real(Bx2))f3=@(eta,kpp,teta)((kpp.^(-8/3)).*(1+2.35*((kpp*eta_s).^(2/3))).*... (w3*w3*exp(-A_t*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))+exp(-A_s*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))-2*w3*exp(-A_ts*(8.284*((kpp*eta_s).^(4/3))+12.978*((kpp*eta_s).^2)))).*... ((exp(1i*k*(p1x*p1x+p1y*p1y-p2x*p2x-p2y*p2y)./(L-eta)).*exp(1i*kpp.*cos(teta)*(p1x-p2x)).*exp(1i*kpp.*sin(teta)*(p1y-p2y)))-(exp(1i*k*(p1x*p1x+p2x*p2x+p1y*p1y+p2y*p2y)./(L-eta)).*exp(1i*kpp.*cos(teta)*(p1x-p2x)).*exp(1i*kpp.*sin(teta)*(p1y-p2y)).*exp(1i*(eta-L).*kpp.*kpp/k))));Bx3=integral3(f3,0,L,0,inf,0,2*pi);BxR3(j)=coeff3*(real(Bx3))j=j+1;endplot(L,BxR1,L,BxR2,L,BxR3);
If you could help me to solve this problem, it will be a big pleasure for me.
Thanks a lot in advance.
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