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I am not quite sure of your parameters. As far as I can make out your equation is [itex]h''+\frac{1}{r}h'=0 [/itex]. Now I wonder: Is r a constant? If so, just integrate and get [itex] h'+\frac{1}{r}h=C[/itex] (C is a constant) and from there [itex]h(x) = C_{2}+C\cdot x + C_{1}e^{\frac{-x}{r}} [/itex]. Nom determine the constants to fit your constraints.num3n said:
The Runge Kutta Method is a numerical method used to solve ordinary differential equations. It is a popular method because it is relatively accurate and easy to implement.
The Runge Kutta Method uses a system of equations to approximate the solution to a differential equation at discrete points. It involves using a series of intermediate steps to better approximate the solution, resulting in a more accurate final answer.
An example of using the Runge Kutta Method is solving the differential equation dy/dx = x + y with initial condition y(0) = 1. This can be solved using the fourth-order Runge Kutta Method, which involves calculating four intermediate values at each step.
MATLAB has built-in functions for solving differential equations, including the Runge Kutta Method. By using the "ode45" function, MATLAB can solve differential equations numerically using the fourth-order Runge Kutta Method.
The Runge Kutta Method is a widely used numerical method because it is relatively accurate, easy to implement, and can handle a wide range of differential equations. It also allows for finer control over the step size, making it more efficient for solving certain types of equations.
