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
      
which represents the behavior of a spring mass system with a mass of m, a spring constant of k and a damping coefficient b.

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 )
where

Licensing:

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

Languages:

ODE_SWEEP_SERIAL is available in a MATLAB version.

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.

FIRE_SERIAL, a MATLAB program which simulates a forest fire over a rectangular array of trees, starting at a single random location. It is intended as a starting point for the development of 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.

SEARCH_SERIAL, a MATLAB program which searches the integers from A to B for a value J such that F(J) = C. this version of the program is intended as a starting point for a parallel approach.

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

Source Code:

Examples and Tests:

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


Last revised on 18 June 2012.