ode_trapezoidal


ode_trapezoidal, a MATLAB code which interactively applies the trapezoidal 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 Euler 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_trapezoidal ( 'x+y', 0.0, 5.0, -3.0, 50 )
      
or, if called with no arguments, it will request them:
        [ xp, yp ] = ode_trapezoidal ( );
        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:

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.
      

Licensing:

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

Languages:

ode_trapezoidal is available in a MATLAB version.

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ode_trapezoidal_test

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Source Code:


Last revised on 30 July 2019.