How to resolve the algorithm Runge-Kutta method step by step in the Crystal programming language

Published on 12 May 2024 09:40 PM
#Crystal

How to resolve the algorithm Runge-Kutta method step by step in the Crystal programming language

Table of Contents

Problem Statement

Given the example Differential equation: With initial condition: This equation has an exact solution:

Demonstrate the commonly used explicit   fourth-order Runge–Kutta method   to solve the above differential equation.

Starting with a given

y

n

{\displaystyle y_{n}}

and

t

n

{\displaystyle t_{n}}

calculate: then:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Runge-Kutta method step by step in the Crystal programming language

Source code in the crystal programming language

y, t = 1, 0
while t <= 10
   k1	=  t         * Math.sqrt(y)
   k2	= (t + 0.05) * Math.sqrt(y + 0.05 * k1)
   k3	= (t + 0.05) * Math.sqrt(y + 0.05 * k2)
   k4	= (t + 0.1)  * Math.sqrt(y + 0.1  * k3)
 
   printf("y(%4.1f)\t= %12.6f \t error: %12.6e\n", t, y, (((t**2 + 4)**2 / 16) - y )) if (t.round - t).abs < 1.0e-5
   y += 0.1 * (k1 + 2 * (k2 + k3) + k4) / 6
   t += 0.1
end

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