mu=1;
f=@(t,x)[x(2);(-mu*(x(1).^2-1).*x(2)-x(1))];
[t,x]=ode45(f,[0,30],[.1;.3]);
plot(t,x)
legend('x','x''')
matlab Consider the Van der Pol oscillator described by * + µ(x? – 1)x +x =...
2. Coupled Differential Equations (40 points) The well-known van der Pol oscillator is the second-order nonlinear differential equation shown below: + au dt 0. di The solution of this equation exhibits stable oscillatory behavior. Van der Pol realized the parallel between the oscillations generated by this equation and certain biological rhythms, such as the heartbeat, and proposed this as a model of an oscillatory cardiac pacemaker. Solve the van der Pol equation using Second-order Runge Kutta Heun's method with the...
Simulate Van der Pol Equation The objective is to simulate the Van der Pol equation which came about with electrical circuits with vacuum tubes. Here are the equations: dy dt dv %Simulation Parameter tend-100; % total simulation time seconds % Initial Conditions %Parameters mu 0.2 Generate two figures. Figure 1 a. Title should state: "Van der Pol Equation" Two plots one above the other: b. Top plot is time vs. y Y-axis should have "y" a. c. Middle plot is...
Consider the following problem Solve for y(t) in the ODE below (Van der Pol equation) for t ranging from O to 10 seconds with initial conditions yo) = 5 and y'(0) = 0 and mu = 5. Select the methods below that would be appropriate to use for a solution to this problem. More than one method may be applicable. Select all that apply. ? Shooting method Finite difference method MATLAB m-file euler.m from course notes MATLAB m-file odeRK4sys.m from...
6. ODE Solvers ODE Initial Value Problems and Systems of ODEs The following is the van der Pol equation: y(0) = yo, y,(0) =Yo The following are solutions curves for two values of the parameter μ. Ignore the green line. Write the solution as a system of equations. Select an appropriate solver for each case, that is, for μ-1 and μ-1000, from the MATLAB list ODE23, ODE45, ODE23s, ODE113, and ODE15s. Give the type of solver and the reason for...
Please provide the matlab code solution for this problem. Exercise 2 Consider the differential equation for the Van der Pol oscillator (use ode45) which has a nonlinear damping term a (y -1) y 1. For E 0.25, solve the equation over the interval 0,50 for initial conditions y (0) 0.1 and y' (0) -1. TASK: Save y as a column vector in the file A04.dat TASK: Save y' as a column vector in the file A05.dat 2. For a 10,...
using matlab thank you 3 MARKS QUESTION 3 Background The van der Pol equation is a 2nd-order ODE that describes self-sustaining oscillations in which energy is withdrawn from large oscillations and fed into the small oscillations. This equation typically models electronic circuits containing vacuum tubes. The van der Pol equation is: dt2 dt where y represents the position coordinate, t is time, and u is a damping coefficient The 2nd-order ODE can be solved as a set of 1st-order ODEs,...
1. (10 points, part I) Consider the following initial boundary value problem lU (la) (1b) (1c) 0L, t> 0 3 cos ( a(x, 0) (a) Classify the partial differential equation (1a) (b) What do the equations (la)-(1c) model? (Hint: Give an interpretation for the PDE, boundary conditions and intial condition.) c) Use the method of separation of variables to separate the above problem into two sub- problems (one that depends on space and the other only on time) (d) What...
solve problem #1 depending on the given information Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...