Ode system Definition and 29 Threads

Hi, I have a set of ODE's represented in matrix format as shown in the attached file. The matrix A has algebraic multiplicity equal to 3 and geometric multiplicity 2. I am trying to find the generalized eigenvector by algorithm (A-λI)w=v, where w is the generalized eigenvector and v is the...

The Coupled ODE Model Below are my coupled differential equations, where the only variable I try to meddle with is the ITMblood. The motivation here is if I try to increase ITMblood (in the next section I will show how I do it), at some concentration of ITMblood (most likely a very huge one) ...

Hi! I'm trying to solve ODE system with 2 equations Here is a result from dsolve. How can i get R(t) out of it And how to substitute initial conditions in it?

Hi PF! Given the ODE system ##x'(t) = A(t) x(t)## where ##x## is a vector and ##A## a square matrix periodic, so that ##A(t) = A(T+t)##, would the following be a good way to solve the system's stability: fix ##t^*##. Then $$ \int \frac{1}{x} \, dx = \int A(t^*) \, dt \implies\\ x(t) =...

Homework Statement This question relates to a very large project I have been assigned in a course on mathematical methods in structural engineering. I have to solve the following equation, in a specific way: (17) Now we have to assume the following solution: (18) It wants me insert...

Hi! \begin{cases} \dot{q} = a \left( 1 - q^2 \right) \\ \dot{a} = - \alpha - a^2 q\end{cases} \qquad \alpha \in (0, 1 ) I've looked into this ODE system about 7 months now, but I've not got anything promising how to write down the solution. I'm mostly interested in q-serie. (To those of you...

Hey there! I was trying to plot a ODE solution, but am not getting what I should be. It is actually plotting the orbit of Earth with Sun at the origin. My equations The (-0.00011847) is GM. The Initial Conditions: The plot I get: Should not I be getting a elliptic/circular plot as the...

I have been solving system of homogeneous ODE numerically using Crank-nicolson (CN) method but now I have a system of non-homogeneous ODE. It would seem that CN would not work since the rank of the matrix will be less than the dimension of the matrix. Is there any other method that can...

dx/dt = x-y^2 dy/dt= x^2 -xy -2x For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it. I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!

Hi everyone I have a system of ODE as follows x1_dot=f1(t)-ax1 x2_dot=f2(t)-ax2 x3_dot=f3(t)-ax3 f1,2,3(t) are unknown nonlinear functions of time, a is constant and unknown, x1,2,3 and their derivatives are given. How can I estimate the parameter a from the given information? Thanks

I need to find a trapping region for the next nonlinear ODE system $u'=-u+v*u^2$ $v'=b-v*u^2$ for $b>0$. What theory i need to use or which code in Mathematica o Matlab could help me to find the optimal trapping region.

Homework Statement Solve the following system for 0<t<5 u^\prime = u-e^{-2t} v, u(0) = 1 v^\prime = u+3v, v(0) = -2 using Forward Euler method and implement the numerical scheme into a MATLAB code. Homework Equations Forward Euler : \vec x^(\prime)_{n+1} = \vec F(t,\vec x)...

Question: Show that the system x'= x-y-x[x^2 + (3/2)y^2] y'= x+y -y[x^2 + (1/2)y^2] has at least one periodic orbit. I know that I need to apply Poincare-Bendixson Theorem. I can prove the first three points of it easily, but to create a trapping region, I believe that I need to...

Hi. If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix: X'=A X, A is a 2x2 matrix. How do I solve this using wolfram or matlab?

Problem: The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter$a$. What is the nature of the Hopf bifurcation that occurs at the critical value of $a$ and state what the critical value is. $\dot{x}=-y+x(a+x^2+(3/2)y^2)$...

Homework Statement The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter a. What is the nature of the Hopf bifurcation that occurs at the critical value of a and state what the critical value is. Homework Equations...

I have: $\dot{x}=4x+y-x(x^2+y^2)$ $\dot{y}=4y-x-y(x^2+y^2)$ And I need to find $\dot{r}$ and $\dot{\theta}$ I got as far as: $\dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4))$ $\dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta))$ How do I go from here to $\dot{r}$ and...

Hello all. I am studying a system and want to investigate how the frequency of y(3) varies under different conditions. However, my the fft I perform on it tells me the frequency is zero, which must be incorrect. I have tried a stack of things but can't see what the problem is. I'm relatively...

hi suppose we have this equation : d/dt(X)=A(t)*X x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients. coefficients of equations and consequently A are depend on t which is time. how i Solve this equation ? thanks

Hello all, I don't have much experience with ODEs. I have a simple system, which I believe is first order linear, similar to the following: dA/dt = 2A + 3B - C dB/dt = A + 2B - C dC/dt = -2A + 5B - 2C Now I would like to include the constraint that A + B + C = 1. How do I do this...

Homework Statement A 3-storey building can be modeled as a system of coupled masses and springs as showen in attached document. Where mi is the mass of each floor, ki is the spring constant, xi is the displacement of each floor, and ci is the damping coeffcient.Homework Equations I understand...

Hi to everyone, I have some problem in implementing a ODE system in matlab. function dC = Model(x,C) dC = zeros(2,1); dC(1) = -2/C(1) -3*dC(2); dC(2) = -3/C(2) -4*dC(1); [x,C] = ode23(@Model(x,C),[0 300],[56.9 0]); plot(x,C) The debugger says "? Input...

Given the ODE system: v' = u(u2-1) u' = v-u Define w=u2+v2. Compute w'. Find the largest radius R for which u2+v2<R so that the if the solution curve (u,v) is inside that circle the solution tends to (0,0) as t--> +\infty Any guidance would be appriciated !

Homework Statement I have 3 masses in 1-D connected by two springs. A driving force is exerted on the first mass and i need to derive the equation of motion of the last mass. I have worked out the Lagrangian to determine the equations of motion but cannot solve for z. Homework Equations The...

Homework Statement Hello. I want to study the stability of the origin of the following problem: dx/dt = -2y dy/dt = x + 2y dz/dt = -2z So the eigenvalues of this 3 x 3 matrix are -2, 1 + i, 1-i. The eigenvectors are (0,0,1) , (2,-1-i,0), (-2,-1+i,0)...

Hi, I need to solve very large complex ODE system. It is about time evaluation of system, which is at time t=0 in eigenstate with the smallest eigenvalue. For my test case I am trying to solve smaller similar problem, the ODE system is like: C^{'}_{m} = - i \sum^{N-1}_{n=0} C_{n}(t) Exp[...

Hi i got a question trying to solve some problems from my schools webpage and encountered a problem where I am given 2 RLC-Circuits and the corresponding dgls for the oscillation ( no problem so for all the standart basic E/M stuff) But then I am asked to transform this system of 2 dgl´s of...

I have a system of spatial ODEs to solve... Actually a DAE system, but here's the issue: The equations are vaild over a specific domain, x = 0..L The equations are only bound at one point (thier "initial point") but at either 0 or L f1(0)=0 f2(0)=100 f3(L)=0 f4(L)=100 (also an...

In order to solve the near field description of a round jet, I want to work out the variables F(\eta) , \rho(\eta) and Y(\eta) which represents the self similar stream function, density, and mass fraction respectively. The system obtained is...