QuestionQuestion

Transcribed TextTranscribed Text

1. Derive the following formula for approximating the derivative and show that is o(h2) by establishing its error term: 3f(x)-4f(x-h)+j(x-2h) - - j'(x) 2 2h 2. Consider the boundary value problem IS" =0, 0Show that the problem has no solution if O # 8. and infinite many solutions when O = 8. 3. (a) Write a MATLAB function that implements the finite difference method for solving the boundary value problem (b) Use the function written in part (a) to solve the boundary value problem 2.x 2 = u(0) =0, u(1) = In(2). The true solution is u(x) Solve the boundary value problem for h = 0.1.0.05,0.025,0.0125, and print the errors of the numerical solution at T = 0.2,0.4.0.6.0.8. Comment on how errors decrease when h is halved. Plot the true solution and the numerical solution for h = 0.05 on the same plot. 4. The general solution of the equation xu" - (2x + 1)z/ + (x+ 1)u = 0 is 21(I) = GIE* + Find the solution of the equation with the boundary conditions u '(0) 1, u'(1) =0 Write down a formula for a discrete approximation of the boundary conditions. Implement the method by modifying the function in Prob- lem 3, and solve the problem with h = 0.1,0.05,0.025,0.0125. Print the errors in a loglog plot and comment on how the error decreases when h is halved.

Solution PreviewSolution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Math Problems Using Matlab Programming
    $40.00 for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Mathematics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats