Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all...
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)
Please help me solve this. thanks 5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h 5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
Estimate the second derivative of the following function using stencils for the FORWARD and CENTRAL derivatives for an order of accuracy of O(h2) for each. Use a step size of h -1. fo)x-2x2 +6 Second derivative, Forward Difference Approximation, o(h2)- Second derivative, Central Difference Approximation, O(h2) Which of the two methods is closer to the true value? (Forward/Central 12.5 points Differential Equation Estimate the second derivative of the following function using stencils for the FORWARD an derivatives for an order...
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...
3. A five-point centered finite difference approximation to the first derivative is given by - f (x + 2h) +8f (x + h) – 8f (x – h) + f(x – 2h) 12h (a) What is the error term associated with this formula? (b) Numerically verify the order of approximation using f(x) = (1 + x2)-1 at x = 1 using the values h = 0.1, 0.01, 0.001.
Using the Taylor series expansion, derive the following 2nd order central difference approximation for the 4th derivative. Please provide answer in clear understandable handwriting dx
Compute a FD second order approximation of the first derivative of the function f(x) = sin(x2) at x = 1.5 using x = 0.1
✓ 4. Derive an order h2 accurate one-sided finite difference approximation to the first derivative dø/dx at the point x = tj. Suppose that the numerical solution di is available at the set of points {C;} and assume constant grid spacing, i.e. h = i+1 - Ti is the same for all i. The derivative must be calculated using ; and only points to its left (i.e. Xj, 2j-1, *;-2, ... use as many as you need). Hint: assume that...
Number 9 requires number 8 so please can you answer both? Thanks. Here's more context: There are also approximations of higher order derivatives that can be computed using only values of the original function. Consider the approximation: u(a + 2h)-2u(a + h) + u (a) h2 8. Using your knowledge of Taylor series, what derivative is approximated by Equa Many different combinations of terms can be used to create approximations to deriva- tion??? What is the order of the approximation?...