please assist 4. (25 pts) Consider a forward-difference approximation for the second derivative of the form Use Taylor's theorem to determine the coefficients A, B, and C that give the maximal...
answer is shown in bold, please show steps to get answer
<13 > Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and find the error f"(x) A=C Af(x-h) +Bf(x) +cf(x+h)
Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and find the error f"(x) A=C Af(x-h) +Bf(x) +cf(x+h)
Consider the standard second order finite difference approximation to the second derivative h2 Let;") =e.mjh for , = 1, M-1.h=r/M. (b) Prove that the farthest eigenvalue from the origin approaches -/h2 as h0 and use this to explain why the ODE systenm du(t) is stiff
Consider the standard second order finite difference approximation to the second derivative h2 Let;") =e.mjh for , = 1, M-1.h=r/M.
(b) Prove that the farthest eigenvalue from the origin approaches -/h2 as h0 and use...
please need help on 8, 9 and 10
8. Use Taylor's Theorem to show that the approximation f 8 f(x+h) - 8f(x – h) - f(x+ 2h) + f (x – 2h) 12h is (h4). # Approximate f'(1.05) using h=0.05 and h = 0.01 in equations (2) and 4). Use the following data: x 1.0 1.04 1.06 1.10 f(x) 1.6829420 1.7732994 1.8188014 1.9103448 | Based on the definition of the derivative, for small values of h, we have the following...
Parts b and c please
4. (25 pts) Given a function f with three continious derivatives, and three equally spaced points zi z, = zi+h, エ3年エ1 + 21, we would like to approxinate f'(z), Let p(z) be the quadratic polynomial interpolating ()) (a) Write p in the Lagrange form. (b) Show the forward difference formula (c) Prove that this expression is a second order approximation off,(r), that is, show that where C depends on the third derivative of f.
4....
3. Consider the following second-order ODE: Using the central difference formula for approximating the second derivative, discretize the ODE (rewrite the equation in a form suitable for solution with the finite difference method) a. b. If the step size is h-0.5, what is the value of the diagonal elements in the resulting matrix of coefficients of the system of linear equations that has to be solved?
Complete all, especially part c and d
(a) Glive the second-order Taylor polynomial T2 ( for the function () about a 16. 4+((X-16)/8)-(1/512) (X-16M2 b) Use Taylor's Theorem to give the Error Term E2(-f()T2) as a function of z and some z between 16 and az (((3/8) Z(-5/2)) (X-16) 3)/6 c) Estimate the domain of values z for which the error E2 () is less than 0.01. Enter a value p for which E2 ()I 0.01 for all 16 16+p,...
Please show all your works.
Thanks.
4.(25 pts) Consider a periodic function X(t) = Sin(3t). Cos . Express x(t) in Exponential Fourier Series form and calculate Fourier Coefficients Co, C1, C-1,C2, C-2 ... etc (as many Fourier Coefficients as needed). What is the fundamental frequency (wo) of the x(t)? (hint: Use Euler's formula to express Sin(.) and Cos(.) in exponential forms)
question b please
Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
Consider the following function rx)=x sin(x), a=0, n= 4, -0.9 0.9 x (a) Approximate fby a Taylor polynomial with degree n at the number a (b) Use Taylor's Inequality to estimate the accuracy of the approximation rx)俗,(x) when x lies in the given interval. (Round M up to the nearest integer. Round your answer to four decimal places.) R4X) 0.00453X (c) Check your result in part (b) by graphing Rn(x)| 0.5 -0.5 -0.001 -0.002 002 0.003 -0.003 0.004 -0.004 0.005...
[T2] This problem concerns the derivation of the equations used to determine the coefficients of a quadratic spline approximation, S(x), to a function F(x) over an interval [x min, Xmax]. To assist in getting the indices correct, it is suggested you draw a picture that displays the labeling of the values involved. In the computational part of this assignment, you will be setting up and solving these equations. • Assume that n panels are used and the knots {x;} are...