I am trying to use matlab's fsolve to solve a system of 4 nonlinear equations. I'm solving the system for each point in a grid of parameters by looping through each point and calling the fsolve function.
My problem is that I need to give some of these parameters as input to fsolve. These inputs should be treated as constants for each separate solving of the system.
Can anyone help me?
you can just do:
result = fsolve(#(x) eqns(a,b,c,d),guess)
and in addition make the function eqns() with your equation set.
Related
I have created a function Euler.m to solve a a system of ODEs using Euler's method. I wish to use this function to solve the system of ODEs defined by the anonymous function func=#(t) ([x(t)+4*y(t)-exp(t);x(t)+y(t)+2*exp(t)]) with initial conditions given by y0.
func=#(t) ([x(t)+4*y(t)-exp(t);x(t)+y(t)+2*exp(t)]);
y0=[4;5/4];
y_exact=#(t) [4*exp(3*t)+2*exp(-t)-2*exp(t);2*exp(3*t)-exp(-t)+exp(t)/4]; %exact solution of ODEs
a=0; % such that
b=1; % a<t<b
N=120;
[t,y] = Euler(func,a,b,y0,N)
However, the following error is displayed:
"Error using solution>#(t)([x(t)+4*y(t)-exp(t);x(t)+y(t)+2*exp(t)])
Too many input arguments.
Error in solution (line 7)
[t,y] = Euler(func,a,b,y0,N)".
Why is this error being displayed?
You are pretending that you already know when writing the ODE function func what the solutions x(t),y(t) are. Then you are going to compute solutions approximations for it. This is completely the wrong way around.
The function for the right side is just for a point in phase space, so you need
func=#(t,y) ([y(1)+4*y(2)-exp(t);y(1)+y(2)+2*exp(t)]);
where the input y is a two-component vector.
im using Matlab to trying to solve 2 equations with 2 variables.
I define the 2 functions, f2(n_1,n_2),f3(n_1,n_2) which both depend on f1(n_1,n_2), then I defined the vectorised function G(n_1,n_2) which contain both of them.
Later I defined a the desired stating point, and tried to solve. but when running the code it raise an error which I'm not fully understand.
the above mentioned is displayed in the code below:
the code:
clear, close all; clc
%Const
N0=25;
G1=1;G2=1;
a1=6;a2=3;
k1=1;k2=4;
%main
syms n_1 n_2
X_0=[-5;5];
f1=N0-a1.*n_1-a2.*n_2;
f2=f1.*G1.*n_1-k1.*n_1;
f3=f1.*G2.*n_2-k2.*n_2;
G=#(n_1,n_2) [f2;f3];
s = fsolve(G,X_0);
the error:
Error using fsolve (line 269)
FSOLVE requires all values returned by functions to be of data type double.
Error in Ex1_Q3_DavidS (line 37)
s = fsolve(G,X_0);
thanks
fsolve is a function that uses numerical methods to find the root of a numerical function.
A numerical function is, for example f=#(x)x^2=2;. In MATLAB, you can evaluate f() at any number and it will return a number, but there is no higher order mathematical abstraction to it. This is however the fastest way to do maths in a computer, as it is not a higher intelligence, just a glorified calculator.
Some people however, want to give higher intelligence to computers and coded very complex symbolic toolboxes that with sets of rules try to teach computers to think semi-like humans and solve symbolic equations, as you do in paper. To solve those equations a function called solve is introduced in MATLAB.
You are doing symbolic math, but using the numeric solver. It does not work, just use the symbolic solver for symbolic math.
I have a symbolic matrix that depends on a complex parameter q. Let the matrix be A(q) and b a column vector. I would like to simultaneously solve the equations
A*b==0; b'*b==1;
using the solve command (preferably the numerical variant vpasolve). The variables to be found are both b and q. I am not quite sure about the syntax on how to do this and would appreciate any help on it. My main problem is that the equation is partially given in matrix form and the searched variable is a vector.
Do I have to resort to fsolve to achieve this? Or is there a way without defining a function?
I was wondering if anyone would tell me if it is possible to solve the coupled equations shown in the attachment using matlab?
I defined first the function of the three equations
function izero= coupled(z,x)
kappa=0.5;
izero=[-kappa*x(1)*(x(2)-x(3));-kappa*x(1)*x(2);kappa*x(1)*x(3)];
end
i want to use bvp4c however i do not have the boundary condition at z=0 for all of the three variables ?? What can I do?
Thank you
I would like to know if anybody knows how I can plot an integral calculated using quad/quadl, or if this is possible.
I read that I can set the trace parameter to be non-zero, and this results in the information of each iteration being provided, but I'm not sure how and if I can use the information to plot an integral.
Thanks.
quad and quadl do not compute an integral function anyway, i.e., an integral as a function of the parameter. And since tools like this work iteratively, refining their estimate until it satisfies a tolerance on the global value, they are not easily made to produce the plot you desire.
You can do what you desire by using a differential equation solver to generate the solution, ode45 for example.