Assignment #3

Assignment Problems (Click on the link to view PDF):

Sample Codes and Illustration :

  1. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/Estimate_error
    Understand how the codes work and learn how to implement the error estimation method we discussed in lectures. When the exact solution is not available, the error can be estimated from two numerical results obtained respectively with step size h and step size h/2.

  2. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/Estimate_order
    Understand how the codes work and learn how to implement the order estimation method we discussed in lectures. When the exact solution is not available, the order of the method can be estimated from three numerical results obtained respectively with step size h, step size h/2 and step size h/4.

  3. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/ODE_Euler
    Understand how the codes work, learn how to implement the Euler method and the backward method, and learn how to do numerical error estimation.

  4. Computer demonstration of the instability of the midpoint method (the leap frog method)
    http://www.cse.ucsc.edu/~hongwang/Codes/Err_propagation

  5. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/ODE_RK
    First run "calc_RK4.m" to generate and save the data. Then run "plot_RK4.m" to read in the data and plot the curve. Run other Runge Kutta methods in the same way.
    Understand how the codes work and learn how to implement the Runge Kutta type methods. Also try to learn how to put two figures on one page.

  6. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/ODE_sys_RK
    First run "calc_sRK4.m" to generate and save the data. Then run "plot_sRK4.m" to read in the data and plot the curve. Run other Runge Kutta methods in the same way.
    understand how the codes work and learn how to implement the Runge Kutta type methods for ODE systems.

  7. Computer demonstration of the advantages of implicit methods in solving stiff ODEs
    http://www.cse.ucsc.edu/~hongwang/Codes/Stiff_ODE

  8. Computer demonstration of the Gibbs phenomenon
    http://www.cse.ucsc.edu/~hongwang/Codes/Interpolation