MATLAB: Ode45

ode45

Hello,

When using ode45, I know I can specify the integrand as a function of time. For instance, dx/dt = cos(t) – x.

Is there a way to alternatively specify the integrand as a set of data points? For instance replace cos(t) with a set of data points that I load.

When I try doing this I'm getting an error. I think because of the internal time steps ode45 uses is different than the times steps in my data points. Changing the tspan input to match the time steps in my data points doesn't seem to make any difference in the internal time steps ode45 uses. Is there any way around this problem?

Thank you, Kevin

Best Answer

This sounds like a job for TRAPZ.

Related Solutions

MATLAB: Parallelized ODE45 solution with 3D spline

Can you just pass the variables spx spy spz to func_xy as additional arguments?

q=1.6e-19;
m=400*1.6e-27;
odeOpts = odeset('Events', @(t,y) myEvent(t,y,tstart))
% pass additional arguments by using function handle:
odefunHandle = @(t,y)func_xy(t,y , q,m,spx,spy,spz)
[t,sol]=ode45(odefunHandle,[0 30e-6],[0;0;y0(j);0;0;0], odeOpts);
%%%
function dxdt=func_xy(t,y , q,m,spx,spy,spz)
% global spx spy spz 
% q=1.6e-19;
% m=400*1.6e-27;
dxdt=[y(2);
    (-q/m)*fnval(spz,{y(1), y(3), y(5)}) ;
     y(4);
    (-q/m)*fnval(spy,{y(1), y(3), y(5)});
     y(6);
    (-q/m)*fnval(spx,{y(1),y(3), y(5)});];
end

By the way are you sure that the main cost of the spline interp is the up-front cost of csapi/fnder, and not the fnval()s?

MATLAB: Convolution on a nonlinearly spaced data set.

Like Matt J says, the usual solution is to get evenly spaced intervals using interpolation, such as interp1() or spline().

Here's a spline demo if you want to do a cubic fit between the points:

% Demo to show spline interpolation.
% Clean up / initialize
clc; 
close all; 
clear all; 
workspace; % Display workspace panel.
% Create the original knot points.
lengthX = 10;
x = 1:lengthX;
y = rand (lengthX,1);
% Plot it and show how the line has sharp bends.
plot(x, y, '-sr', 'LineWidth', 2);
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Use splines to interpolate a smoother curve,
% with 10 times as many points,
% that goes exactly through the same data points.
samplingRateIncrease = 10;
newXSamplePoints = linspace(1, lengthX, lengthX * samplingRateIncrease);
smoothedY = spline(x, y, newXSamplePoints);
% Plot smoothedY and show how the line is
% smooth, and has no sharp bends.
hold on; % Don't destroy the first curve we plotted.
plot(newXSamplePoints, smoothedY, '-ob');
title('Spline Interpolation Demo', 'FontSize', 20);
legend('Original Points', 'Spline Points');
% Mathworks Demo code from their Help
% x = 0:10;
% y = sin(x);
% xx = 0:.25:10;
% yy = spline(x,y,xx);
% plot(x,y,'o',xx,yy)

The input points don't need to be uniformly spaced like I did in the demo.

Best Answer

Related Solutions

MATLAB: Parallelized ODE45 solution with 3D spline

MATLAB: Convolution on a nonlinearly spaced data set.

Related Question