Practical MATLAB Modeling with Simulink by Sulaymon L. Eshkabilov

Author:Sulaymon L. Eshkabilov
Language: eng
Format: epub
ISBN: 9781484257999
Publisher: Apress

Example 1

Here is the example problem: .

with the initial condition . The given ODE can be rewritten in the form of an implicit differential equation expressed in Equation (8.44), as shown here:

Subsequently, this can also be expressed as follows:

and as follows:

Note that the expression of F(t, y, dy) = 0 is the main difference in defining F in implicit ODEs from explicit ones. In this example, the F function, containing three arguments (which are ), can be expressed via an anonymous function (@) directly. Here is the complete solution, called IMPLICIT_1ODE_EX1.m:% IMPLICIT_1ODE_EX1.m

%{

EXAMPLE 1. Problem: t^2*y'+t*(y')^2+2*cos(t)=1/y with ICs: y(0)=1/2;

Part 1.

The problem function is defined via function handle under name of Yin.

A new variable is introduced: dy=yp.

%}

clearvars; close all

Yin=@(t,y, yp)(t^2*yp+t*yp^2+2*cos(t)-1/y);

y0=1/2; yp0=0; % Initial conditions

[t, yt]=ode15i(Yin, [0, 6*pi], y0, yp0);

plot(t, yt, 'bo-')

title('\it Simulation of: $$ t^2*\frac{dy}{dt}+t*(\frac{dy}{dt})^2+2*cos(t)=y^{-1}, y_0=\frac{1}{2} $$', 'interpreter', 'latex')

grid on;

xlabel('\it t'),

ylabel( '\it Solution, y(t)'),

hold on

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