How to solve complex 1st order ODEs in octave/Matlab

In summary, to solve a 2 complex 1st order ODEs using octave/matlab, you need to decompose the ODEs into real and imaginary parts and create a new system of variables using the real and imaginary parts.
  • #1
alan_liu
1
0
I am stuck with the issue quite sometimes already.
The question is to solve a 2 complex 1st order complex ODEs.
The hints that given by the professor is to separate the ODEs into the real and imaginary part as ocatve/matlab only capable of handling real ODEs with “ isode “ function.


So how to decompose a complex ODEs into real and imaginary part? For instance, a real complex ODEs can be decomposed into 2 functions, 1 with all the real part, and other one with all the imaginary part.
Please do let me know if i am not stated the problems clearly as well.

Any hints and reference materials will be truly appreciated.
 
Physics news on Phys.org
  • #2
Hi Alan, welcome to PF!

If you have two complex ODEs for variables ##y_1## and ##y_2##, define a new system of variables
$$
\begin{align}
u_1 &= \Re (y_1) \\
u_2 &= \Im (y_1) \\
u_3 &= \Re (y_2) \\
u_4 &= \Im (y_2)
\end{align}
$$
substitute the ##u##'s for the ##y##'s in your ODEs, and this should give you a system of 4 ODEs for the ##u##'s.
 

1. How do I define the differential equation in octave/Matlab?

In order to solve a first order ordinary differential equation (ODE) in octave/Matlab, you must first define the differential equation using symbolic variables. This can be done using the syms function, which allows you to create symbolic variables for the independent variable (usually t) and the dependent variable (usually y). For example, to define the differential equation dy/dt = t*y, you would use the following code:
syms t y.
This creates symbolic variables t and y that can be used in your differential equation.

2. How do I specify initial conditions for the ODE?

In order to solve a first order ODE, you must also specify initial conditions. These are the values of the dependent variable at a particular point in the independent variable. This can be done using the odeToInitial function in octave/Matlab. This function takes the differential equation and initial conditions as inputs and returns a new differential equation that can be solved using the ode45 function. For example, if your initial condition is y(0) = 1, you would use the following code:
odeToInitial(@(t,y) t*y, 0, 1).
This creates a new differential equation that can be solved using ode45.

3. What is the difference between Euler's method and Runge-Kutta methods?

Euler's method is a first-order numerical method for solving differential equations, while Runge-Kutta methods are higher-order methods that use multiple evaluations of the differential equation at different points to improve accuracy. Euler's method is simpler to implement but can be less accurate, while Runge-Kutta methods are more accurate but require more computations.

4. How do I plot the solution to a first order ODE in octave/Matlab?

After using the ode45 function to solve the differential equation, you can use the plot function to plot the solution. The ode45 function returns two arrays, one for the independent variable and one for the dependent variable. You can use these arrays to plot the solution using the following code:
t = linspace(0,10);
[t,y] = ode45(@(t,y) t*y, t, 1);
plot(t,y).
This code creates a time array t from 0 to 10 and uses it to solve the differential equation with the initial condition y(0) = 1. The plot function is then used to plot the solution.

5. How do I handle complex solutions when solving ODEs in octave/Matlab?

Some ODEs may have complex solutions, which can be difficult to handle in octave/Matlab. One approach is to use the real and imag functions to separate the real and imaginary parts of the solution. Another approach is to use the odeToVectorField function to convert the complex ODE into a system of real ODEs, which can then be solved using ode45. Additionally, you can use the ode45s function, which is specifically designed to handle stiff systems of ODEs with complex solutions.

Similar threads

Difficulties solving ODE in Octave
    • MATLAB, Maple, Mathematica, LaTeX
Replies
6
Views
2K
MATLAB How to Plot y=sin(x)/log(x) in MATLAB Without Imaginary Errors?
    • MATLAB, Maple, Mathematica, LaTeX
Replies
11
Views
2K
Complex numbers problem |z| - iz = 1-2i
    • Precalculus Mathematics Homework Help
Replies
20
Views
908
Solving Coupled First Order ODEs: Is There a Closed Form Solution?
    • Differential Equations
Replies
28
Views
2K
ODE solver for second Order ODE with Stiffness and Mass Matrices
    • Mechanical Engineering
Replies
3
Views
1K
MATLAB Solving a Complex Second-Degree Ode with Bessel Functions | MATLAB Help
    • MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
2K
I Real ODE yields real solution through complex numbers
    • Differential Equations
Replies
3
Views
2K
Partial fraction decomposition with Laplace transformation in ODE
    • Calculus and Beyond Homework Help
Replies
9
Views
1K
Help with Octave for system of ODEs
    • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
2K
Solve 3 Coupled ODEs with NDSolve - Error Fix & Alternatives
    • MATLAB, Maple, Mathematica, LaTeX
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top