The differential equation system is given as follows:
ODE 1: y1′ = f(x, y1, y2, y3)
ODE 2: y2′ = g(x, y1, y2, y3)
ODE 3: y3′ = h(x, y1, y2, y3)
The solution of the differential equations is calculated numerically. The used method can be selected. Three Runge-Kutta methods are available: Heun, Euler and Runge-Kutta 4.Order. The initial values y01, y02 and y03 can be varied with the sliders on the vertical axis at x0 in the chart. The value for x0 can be set in the numeric input field. In the input fields for the functions f(x, y1, y2, y3), g(x, y1, y2, y3) and h(x, y1, y2, y3), up to three parameters a, b and c can be used and changed by the sliders in the graph.
f(x,y1,y2,y3)=
g(x,y1,y2,y3)=
h(x,y1,y2,y3)=
| Function | Description |
|---|---|
| sin(x) | Sine of x |
| cos(x) | Cosine of x |
| tan(x) | Tangent of x |
| asin(x) | arcsine |
| acos(x) | arccosine of x |
| atan(x) | arctangent of x |
| atan2(y, x) | Returns the arctangent of the quotient of its arguments. |
| cosh(x) | Hyperbolic cosine of x |
| sinh(x) | Hyperbolic sine of x |
| pow(a, b) | Power ab |
| sqrt(x) | Square root of x |
| exp(x) | e-function |
| log(x), ln(x) | Natural logarithm |
| log(x, b) | Logarithm to base b |
| log2(x), lb(x) | Logarithm to base 2 |
| log10(x), ld(x) | Logarithm to base 10 |
The general ODE third order is:
y′′′ = f(x, y, y′, y′′)
With a substitution the differential equation of 3.order can be transformed to a differential system of first order.
Substitution:
y1 = y
y2 = y′
y3 = y′′
So the resulting ODE system of 1.order is:
y1′ = y2
y2′ = y3
y3′ = f(x, y1, y2, y3)
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