I'm trying to solve the following equation with respect to b
I need to find the value of b code is
clear allE=1.5e8;syms b a0=-4e7/400;T0=600;T=300;temp=1/(2*a0*(T0-T));X=5050700286489334129256038400000/(4349164374701853503175341475971*b) + exp(erfinv(erf(pi/b)/2 + (633825300114114700748351602688*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b) - ((erf(pi/b) - (1267650600228229401496703205376*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b))^2 + 1/5)^(1/2)/2)^2)*exp(-(2*b*erfinv(erf(pi/b)/2 + (633825300114114700748351602688*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b) - ((erf(pi/b) - (1267650600228229401496703205376*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b))^2 + 1/5)^(1/2)/2) - b^2*1i)^2/(4*b^2))*(50507002864893341292560384/(4349164374701853503175341475971*b) + (50507002864893341292560384*(erf(pi/b) - (1267650600228229401496703205376*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b)))/(4349164374701853503175341475971*b*((erf(pi/b) - (101014005729786682585120768*E + 4040560229191467303404830720000000)/(4349164374701853503175341475971*b))^2 + 1/5)^(1/2))) + exp(erfinv(erf(pi/b)/2 + (633825300114114700748351602688*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b) - ((erf(pi/b) - (1267650600228229401496703205376*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b))^2 + 1/5)^(1/2)/2)^2)*exp(-(2*b*erfinv(erf(pi/b)/2 + (633825300114114700748351602688*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b) - ((erf(pi/b) - (1267650600228229401496703205376*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b))^2 + 1/5)^(1/2)/2) + b^2*1i)^2/(4*b^2))*(50507002864893341292560384/(4349164374701853503175341475971*b) + (50507002864893341292560384*(erf(pi/b) - (1267650600228229401496703205376*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b)))/(4349164374701853503175341475971*b*((erf(pi/b) - (101014005729786682585120768*E + 4040560229191467303404830720000000)/(4349164374701853503175341475971*b))^2 + 1/5)^(1/2))) + (5050700286489334129256038400000*(erf(pi/b) - (1267650600228229401496703205376*((5879788993030477*E)/73786976294838206464 + 459358515080506015625/144115188075855872))/(4349164374701853503175341475971*b)))/(4349164374701853503175341475971*b*((erf(pi/b) - (101014005729786682585120768*E + 4040560229191467303404830720000000)/(4349164374701853503175341475971*b))^2 + 1/5)^(1/2)) + 7737125245533627/9671406556917033397649408 vpasolve(X==temp,b)
but matlab(2016 version) gives the following error:
ans =Empty sym: 0-by-1
equation also contain imaginary part which is written 1i in the expression of X
please help me for the same code for the calculation of X given below please have a look maybe this can help, code for the calculation of X is:
clear allsyms E b;N0=1e6;E0=1e8;Eeff=-0.4e8;a=19.3567;p=0.1;ed=0.4e-9;efe=4.5*1e6*8.854e-12;x=2*efe*(E-Eeff)/(a*b*p*sqrt(pi));xm=erf(pi/b);delta=0.05;H_f=x-0.5*(x-xm+sqrt((x-xm).^2+4*delta));theta=b*erfinv(H_f);N1=N0*p;J=N1*erf(pi/b);p1=0.5*N1*exp(-b*b*0.5);P_diel=2*ed*(E-E0);p2=erf((2*theta+i*b*b)/(2*b))+erf((2*theta-i*b*b)/(2*b))+N1*erf(theta/b);%+P_diel;
P=p1+p2+P_diel;X= diff(P,E);
Best Answer