Apply Runge kutta method of fourth order
Answers
Answer:
Runge-Kutta 4th Order Method to Solve Differential Equation
Given following inputs,
An ordinary differential equation that defines value of dy/dx in the form x and y.
Initial value of y, i.e., y(0)
Thus we are given below.
\frac{\mathrm{dx} }{\mathrm{d} y} = f(x, y),y(0)= y_o
The task is to find value of unknown function y at a given point x.
The Runge-Kutta method finds approximate value of y for a given x. Only first order ordinary differential equations can be solved by using the Runge Kutta 4th order method.
Below is the formula used to compute next value yn+1 from previous value yn. The value of n are 0, 1, 2, 3, ….(x – x0)/h. Here h is step height and xn+1 = x0 + hRunge-Kutta 4th Order Method to Solve Differential Equation
Given following inputs,
An ordinary differential equation that defines value of dy/dx in the form x and y.
Initial value of y, i.e., y(0)
Thus we are given below.
\frac{\mathrm{dx} }{\mathrm{d} y} = f(x, y),y(0)= y_o
The task is to find value of unknown function y at a given point x.
The Runge-Kutta method finds approximate value of y for a given x. Only first order ordinary differential equations can be solved by using the Runge Kutta 4th order method.
Below is the formula used to compute next value yn+1 from previous value yn. The value of n are 0, 1, 2, 3, ….(x – x0)/h. Here h is step height and xn+1 = x0 + h