**ode_euler**,
a MATLAB code which
interactively applies the Euler method to estimate the solution
of an ordinary differential equation (ODE) y'=f(x,y), over the interval [a,b],
with initial condition y(a)=ya, using n steps.

The user enters a formula for f(x), the values of a and b, the initial condition ya, and the value of n.

The program divides [a,b] into n equal intervals, and takes n steps. It returns arrays xp and yp containing n+1 pairs of values that can be plotted.

The program can be invoked by a function call, in which case the string specifying f(x) must be quoted:

[ xp, yp ] = ode_euler ( 'x+y', 0.0, 5.0, -3.0, 50 )or, if called with no arguments, it will request them:

[ xp, yp ] = ode_euler ( ); Enter function formula, like x*y: x+y Enter left limit, a: 0.0 Enter right limit, b: 5.0 Enter initial condition: -3.0 Enter number of steps: 50

The function is specified as a string which is either:

- a MATLAB expression using the arguments 'x' and 'y';
- the name of an M-file followed by the arguments '(x,y)'.

The string should not contain any spaces between symbols, except when it is passed as a function argument in quotes.

It is not necessary to use the "dot" notation for expressions involving '*', '/', or '^', but it doesn't hurt either.

Examples of function specifications:

y 2*exp(x)-2*y x*y^2 sin(x)*sqrt(y)/8 wiggle(x,y) <-- where "wiggle.m" is a user-provided M file.

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

**ode_euler** is available in
a MATLAB version and
a Python version.

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- ode_euler.m the source code.