ODE_SWEEP_SERIAL
Analyze an ODE Solution for Many Parameter Values

ODE_SWEEP_SERIAL is a directory which computes the solution of an ODE for many parameter values, keeping track of the maximum absolute value of the solution.

Consider the parameterized second order differential equation:

        m x'' + b x' + k x = 0
      

We now suppose that we are interested in properties of the solution x(t) over the time interval from 0 to 25 seconds, as we vary the physical properties b and k. In particular, we would like to know the maximum value of x(t) over the time interval for each choice of the physical parameters.

To answer this question, we must solve the ODE for each choice of the parameters.

The basic function has the form:

function peakVals = ode_fun ( bVals, kVals )

• bVals is an array of B values;
• kVals is an array of K values;
• peakVals is an array containing the maximum value of the ODE solution for each combination of B and K.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

COLLATZ, a MATLAB library which computes and analyzes the Collatz sequence (or "hailstone" sequence or "3n+1 sequence");

FFT_SERIAL, a MATLAB program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for implementing a parallel version.

MD, a MATLAB program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.

MXM, a MATLAB program which sets up a matrix multiplication problem A=B*C, intended as a starting point for implementing a parallel version.

POISSON_SERIAL, a MATLAB program which computes an approximate solution to the Poisson equation in a rectangle, and is intended as the starting point for the creation of a parallel version.

PRIME_SERIAL, a MATLAB program which counts the number of primes between 1 and N, intended as a starting point for the creation of a parallel version.

QUAD_SERIAL, a MATLAB program which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.

QUAD2D_SERIAL, a MATLAB program which approximates an integral over a 2D region using a product quadrature rule, and is intended as a starting point for parallelization exercises.

SATISFY, a MATLAB program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

TIMER, MATLAB programs which demonstrate how to compute CPU time or elapsed time.

Source Code:

• ode_fun.m, the function which performs the calculations.
• ode_system.m, a function which redefines the second order ODE as a pair of first order ODE's, suitable for treatment by MATLAB's ODE solvers.
• ode_display.m, a script which displays a contour plot of the results of the parameter sweep.

Examples and Tests:

• ode_script.m, sets up a parameter sweep and runs the code.
• ode_script_output.txt, the output file.
• ode_display.png, a surface plot of the data XMAX(B,K) computed by the program.

You can go up one level to the MATLAB source codes.