DEW1 draws the solution of differential equation of first order with initial values t0 and y0. The program also draws the direction field.
Drawing (Initial values)
Solution is drawn with initial values t0 and y0. Values can be entered in the t= and y= text fields, then clicking the Draw-button will draw the corresponding solution. Or the initial conditions can be clicked on with the mouse.
A differential equation may be selected from the pre-defined examples or may by defined by user. For example, the equation
y' - 3*y + 2*t = 0
is first solved for y':
y' = 3*y - 2*t,
then the right side of equation is given to the program:
3*y - 2*t.
Finally click the Read equation-button.
Changing the scale (Scale)
The scale can be adjusted by chancing the values of tmin, tmax, ymin and ymax and clicking the Change scale -button.
Numerical method (General)
The solution may be plotted by using one of the following algoritms: adaptive Runge-Kutta, Euler, improved Euler, Runge-Kutta or Adams-Bashforth.
For non-adaptive methods the stepsize may be adjusted via the Stepsize -textfield.
Clear -button clears everything that has been drawn.
The equation parser recognizes the following mathematical operations, elementary functions and variables:
-Basic operations: +, -, *, /, and power ^.
-Trigonometrical functions: sin(), cos(), tan(), asin(), acos(), atan().
-Elementary functions: exp(), abs(), sqrt() and log().
-Other functions: abs(), sign().
-Variables: t, y.
There must always be an operator between two operands. For example, 2t+3y must be given to the program in the form of 2*t+3*y.