# ODE 45 couldn't solve the differential equation.

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Abhiram CD on 8 Aug 2021
Answered: darova on 9 Aug 2021
I have a differential equation of pump power of eerbium wave guide. The ODE should be solved in matlab. I dont know how to use ODE properly. I have solved only simple ODE in matlab.if you can check it. please.
This is my code.
clc
clear
close all
L=10;
z=0:0.1:L;
Nt = [1.2*10^(20), 1.2*10^(20), 1.2*10^(20)];
ap=0.23e2;
sca=2.1e-25;
Tp=0.85;
Tcb = 30*10^(-6);
Tba = 2.3*10^(-3);
vs=196e12;
vp=307e12;
h=6.625*10^(-34);
Pp0=10^(-3);
Ps0=10^(-6);
sab=4.8e-2;
sac=2.1e-21;
sba=4.4e-21;
Is=Ps0*exp(-ap)/(2*pi*0.8e-8);
Ip=Pp0*exp(-ap*z)/(2*pi*0.8e-8);
Wab=Is*sab/h*vs;
Wac=Ip*sac/h*vp;
Wba=Is*sba/h*vs;
nb=((Wab+Wac)/1+Wac*Tcb)/(Wab+Wba+(1/Tba)+(Wac*(1-Wab*Tcb)/(1+Wac*Tcb)));
nc=(Wac*Tcb*(1-nb)')./(1+Wac*Tcb);
na=1-nb-nc;
for k = 1:3
ode_ = @(z,Pp) (-ap + (((sca*nc)-(sac*na))*Tp*Nt(k)*Pp))';
PSol(z) = ode45(ode_, [0 L], 0);
Pp_sol(k) = PSol;
end
I need the solution of Pp in three different Nt valus. that is why I have given a for loop. this gives me an error.
% Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.
%
% Error in ode (line 42)
% Pp_sol(k) = PSol;
The z values can't be given as an array. Then it gave me another error,
% Error using odearguments (line 95)
% @(Z,PP)(-AP+(((SCA*NC)-(SAC*NA))*TP*NT(K)*PP))' returns a vector of length 101, but the length of initial conditions
% vector is 1. The vector returned by @(Z,PP)(-AP+(((SCA*NC)-(SAC*NA))*TP*NT(K)*PP))' and the initial conditions vector
% must have the same number of elements.
%
% Error in ode45 (line 115)
% odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
%
% Error in ode (line 41)
% PSol(z) = ode45(ode_, [0 L], 0);
I have given it as a random alue to check if the loop is working.

darova on 9 Aug 2021
Try this way
psol = [];
for k = 1:3
ode_ = @(z,Pp) (-ap + (((sca*nc)-(sac*na))*Tp*Nt(k)*Pp))';
psol = [psol; ode45(ode_, [0 L], 0)];
end