1. System of Ordinary Differential Equation using Runge-Kutta fourth-order formula(RK4)
Solving of First-Order Two Differential Equation Y'(t)=F(t,x,y) and X'(t)=F(t,x,y) IVP(Initial Value Problem).
Source code in C#.
2. Third-Order Differential Equation
Using Runge-Kutta fourth-order formula(RK4)
Diff equation Y'''(t)=F(t,y,y',y'') use IVP(Initial Value Problem).
Source code in C#.
3.Linear Shooting Method
To approximate the solution of the boundary value problem (bvp) x '' = p(t) x'(t) + q(t) x(t) + r(t) with x(a) = alpha and x(b) = beta over the interval [a, b], subinterval M by using the Runge-Kutta method of order 4.
Source code in Lazarus/pascal.
4. Second-order ODE Solver using Runge-Kutta-Fehlberg (RKF45)
To solving initial value problem (ivp) second-order Ordinary Differential Equation(ODE) using Runge-Kutta-Fehlberg formula (RKF45). This formula got advantages than the RK4 classic, RKF45 have Error Estimation. In this python project, use math parser pymep, so we can input equation at runtime.
from pymep.realParser import eval
# e.g. slope g1
var = {"x": x[k], "y": Yk[k], "z":
Yk_dash[k]}
g1 = h*eval(DiffEquation, var)5. ODEs Solver
First-Order Ordinary Differential Equation (ivp) using Runge-Kutta 4th Order(RK4) method.
To approximate the solution of the initial value problem (ivp) y ' =f(x,y) with y(a)=yo over [a,b] and subinterval M.
Source code in Delphi.
6. Fourth-Order ODEs Solver
Fourth-Order Ordinary Differential Equation (ivp) using Runge-Kutta 4th Order(RK4) method.
To approximate the solution of the initial value problem (ivp)
y '''' =f(t,y,y',y'',y''') with initial condition y(t0), y'(t0), y''(t0) & y'''(t0) known as starting points, over [a,b] and subinterval M.
As the result we got values y,y',y'' and y'''(plot in graph).
Source code in Lazarus.
7. System of Third-Order ODEs Solver
System of Third-Order Ordinary Differential Equation (ivp) using Runge-Kutta 4th Order(RK4) method.
To approximate the solution of the initial value problem (ivp)
x'''= f(t,x,y,z,x',y',z',x'',y'',z'')
y'''= g(t,x,y,z,x',y',z',x'',y'',z'')
z'''= h(t,x,y,z,x',y',z',x'',y'',z'')
with initial condition x(t0), y(t0), z(t0), x'(t0), y'(t0), z'(t0) x''(t0), y''(t0) and z''(t0) known, over [a,b] and subinterval M.
As the result we got values x,y,z,x',y',z',x'',y'' and z'' that ploted in the graph.
Source code in Lazarus.