# Call a function with multiple nonlinear eqns with ODE45

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Anthony Sirico on 26 Mar 2021
Edited: Star Strider on 27 Mar 2021
I created a function with multiple nonlinear equations, and inside that function i call on another function that uses a time parameter. In the script, I use ode45 to simulate the equations, but I get the following error:
Error using odearguments (line 95)
@(T,X)FNONLINEAR(TSPAN) returns a vector of length 1, but the length of initial conditions vector is 4. The vector returned by @(T,X)FNONLINEAR(TSPAN) 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);
I use the following code:
close all; clear; clc
tspan = [0 150];
x0 = [1;0;0;0];
[t,y] = ode45(@(t,x) fnonlinear(tspan),tspan,x0)
plot(t,y)
function DX = fnonlinear(t)
[ap,bp,am,bm,r,gamma] = problem_parameters(t);
thetah1 = bm/bp;
thetah2 = (am-ap)/bp;
u = @(t,x) thetah1*r+thetah2*x;
dx1 = @(t,x1) ap*x1+bp*u(t,x);
dx2 = @(t,x2) am*x2+bm*r;
dx3 = @(x1,x2) -gamma*(x1-x2)*r;
dx4 = @(x1,x2) -gamma*(x1-x2)*x1;
DX = @(t,x) [dx1(t,x);dx2(t,x);dx3(t,x);dx4(x1,x2)];
end
function [ap,bp,am,bm,r,gamma] = problem_parameters(t)
% problem parameters
bp = 2; am = -1; bm = 1; r = 0.5; gamma = 2;
% simulate a fault at 100 s
if t >= 100
ap = 2;
else
ap = 1; % fault causes reduced value of ap
end
end
Please let me know if i need to clarify anything.

Star Strider on 27 Mar 2021
There were a number of errors that I corrected.
This runs and produces what appears to be appropriate output:
tspan = [0 150];
x0 = [1;0;0;0];
[t,y] = ode45(@(t,x) fnonlinear(t,x),tspan,x0);
figure
plot(t,y)
grid
xlim([0 8]) % Optional
function DX = fnonlinear(t,x)
[ap,bp,am,bm,r,gamma] = problem_parameters(t);
thetah1 = bm/bp;
thetah2 = (am-ap)/bp;
u = @(x) thetah1*r+thetah2*x;
dx1 = ap*x(1)+bp*u(x(1));
dx2 = am*x(2)+bm*r;
dx3 = -gamma*(x(1)-x(2))*r;
dx4 = -gamma*(x(1)-x(2))*x(1);
DX = [dx1;dx2;dx3;dx4];
end
function [ap,bp,am,bm,r,gamma] = problem_parameters(t)
% problem parameters
bp = 2; am = -1; bm = 1; r = 0.5; gamma = 2;
% simulate a fault at 100 s
if t >= 100
ap = 2;
else
ap = 1; % fault causes reduced value of ap
end
end
.
Star Strider on 27 Mar 2021
If that does what you want, code it accordingly, and add another argument to ‘u’, and create ‘u’ as a function of both arguments.
Note that ‘u’ as originally written is only a function of ‘x’ (since ‘r’ already exists in the workspace, ‘u’ inherits that value and an explicit argument for it is not necessary), so passing ‘u’ an additional argument without changing its internal coding will likely not change its result.

R2020b

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