Runge 4 th Order Method Chemical Engineering Majors

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Runge 4 th Order Method Chemical Engineering Majors Authors: Autar Kaw, Charlie Barker http:

Runge 4 th Order Method Chemical Engineering Majors Authors: Autar Kaw, Charlie Barker http: //numericalmethods. eng. usf. edu Transforming Numerical Methods Education for STEM Undergraduates 2/19/2021 http: //numericalmethods. eng. usf. edu 1

Runge-Kutta 4 th Order Method http: //numericalmethods. eng. usf. edu

Runge-Kutta 4 th Order Method http: //numericalmethods. eng. usf. edu

Runge-Kutta 4 th Order Method For Runge Kutta 4 th order method is given

Runge-Kutta 4 th Order Method For Runge Kutta 4 th order method is given by where 3 lmethods. eng. usf. edu http: //numerica

How to write Ordinary Differential Equation How does one write a first order differential

How to write Ordinary Differential Equation How does one write a first order differential equation in the form of Example is rewritten as In this case 4 lmethods. eng. usf. edu http: //numerica

Example The concentration of salt, in a home made soap maker is given as

Example The concentration of salt, in a home made soap maker is given as a function of time by At the initial time, t = 0, the salt concentration in the tank is 50 g/L. Using Euler’s method and a step size of h=1. 5 min, what is the salt concentration after 3 minutes. 5 lmethods. eng. usf. edu http: //numerica

Solution Step 1: 6 lmethods. eng. usf. edu http: //numerica

Solution Step 1: 6 lmethods. eng. usf. edu http: //numerica

Solution Cont is the approximate concentration of salt at 7 lmethods. eng. usf. edu

Solution Cont is the approximate concentration of salt at 7 lmethods. eng. usf. edu http: //numerica

Solution Cont Step 2: 8 lmethods. eng. usf. edu http: //numerica

Solution Cont Step 2: 8 lmethods. eng. usf. edu http: //numerica

Solution Cont is the approximate concentration of salt at 9 lmethods. eng. usf. edu

Solution Cont is the approximate concentration of salt at 9 lmethods. eng. usf. edu http: //numerica

Solution Cont The exact solution of the ordinary differential equation is given by The

Solution Cont The exact solution of the ordinary differential equation is given by The solution to this nonlinear equation at t=3 minutes is 10 lmethods. eng. usf. edu http: //numerica

Comparison with exact results Figure 1. Comparison of Runge-Kutta 4 th order method with

Comparison with exact results Figure 1. Comparison of Runge-Kutta 4 th order method with exact solution 11 lmethods. eng. usf. edu http: //numerica

Effect of step size Table 1 Value of concentration of salt at 3 minutes

Effect of step size Table 1 Value of concentration of salt at 3 minutes for different step sizes Step size, 3 1. 5 0. 75 0. 375 0. 1875 14120 11455 25. 559 10. 717 10. 715 − 14109 − 11444 − 14. 843 − 0. 0014969 − 0. 00031657 131680 106800 138. 53 0. 013969 0. 0029544 (exact) 12 lmethods. eng. usf. edu http: //numerica

Effects of step size on Runge. Kutta 4 th Order Method Figure 2. Effect

Effects of step size on Runge. Kutta 4 th Order Method Figure 2. Effect of step size in Runge-Kutta 4 th order method 13 lmethods. eng. usf. edu http: //numerica

Comparison of Euler and Runge. Kutta Methods Figure 3. Comparison of Runge-Kutta methods of

Comparison of Euler and Runge. Kutta Methods Figure 3. Comparison of Runge-Kutta methods of 1 st, 2 nd, and 4 th order. 14 lmethods. eng. usf. edu http: //numerica

Additional Resources For all resources on this topic such as digital audiovisual lectures, primers,

Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, Math. Cad and MAPLE, blogs, related physical problems, please visit http: //numericalmethods. eng. usf. edu/topics/runge_kutt a_4 th_method. html

THE END http: //numericalmethods. eng. usf. edu

THE END http: //numericalmethods. eng. usf. edu

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