WEEK10
July 12 and July 14th

This page contains lectures, examples and assignments for the class "Introduction to Scientific Programming".

Lectures:

• Lecture #18, "The Euler Method for the Initial Value Problem"
• Lecture #19, "The Midpoint and Runge Kutta Methods"

Examples:

• baby_bust.png, a plot of the population growth for Lab Exercise 9. I used some extra gnuplot commands:

            gnuplot
              set grid
              set xlabel "Year"
              set ylabel "Population"
              set title "Lab Exercise 9, the Baby Bust Equation"
              plot "pop.txt" using 1:2 with lines
            quit
            

• euler.cpp, a function to take one Euler step.
• euler_f1.cpp, a program which solves the baby boom problem between 2011 and 2020, using the Euler method.
• euler_f2.cpp, a program which solves the baby bust problem from 1850 to 2000, using the Euler method.
• euler_f3.cpp, a program which solves the wiggly problem between 0 and 12 * pi, using the Euler method.
• euler_f4.cpp, a program which solves the predator-prey problem, involving two variables, using the Euler method.
• f1.cpp, a function which evaluates the derivative for example 1, the "baby boom" equation.
• f2.cpp, a function which evaluates the derivative for example 1, the baby-bust equation.
• f3.cpp, a function which evaluates the derivative for example 3, the "wiggly" equation.
• f4.cpp, a function which evaluates the derivative for example 4, the predator-prey problem.
• f7.cpp, a function which evaluates the derivative for example 7, the pendulum equation.
• midpoint.cpp, a function which carries out the midpoint method for a single ODE.
• midpoint_f3.cpp, a program which uses the midpoint method to solve the single ODE in the wiggly equation.
• midpoint_f4.cpp, a program which uses the midpoint method to solve the two first order ODE's associated with the predator-prey equation.
• midpoint_f7.cpp, a program which uses the midpoint method to solve the two first order ODE's associated with the single second order ODE that is the pendulum equation.
• rk4.cpp, a function which takes a single Runge-Kutta step for a single ODE.
• rk4.hpp, the "include file" which defines the single function in the file rk4.cpp.
• rk4_f3.cpp, a program which uses the Runge-Kutta method to solve the single ODE in the wiggly equation.

Assignments:

• Project description, can be one line or one paragraph, but you must choose and describe a final project and email me the description by Tuesday, July 12.
• In class exercise #9, on Tuesday: Solve and plot the "baby bust" equation.
• Program Homework #7 is due on Thursday. Please mail your program and output to Detelina.
• Program Homework #8, to be assigned on Thursday, will be due on July 21st.

You can go up one level to the ISC course page.