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Compute forward and backward difference approxi- aion 21.1 ns of O(h) and Oh), and central difference approxi- mations of 0(h2) and O(h) for the first derivative of y sin x at π/ 12. Estimate the...
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...
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...
Use forward and backward difference approximations of O(h)
Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h2) to estimate the first derivative of the following function:f(x)=25x³-6x²+7x-88Evaluate the derivative at x=2 using a step size of h=0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.
use radians in trig functions Estimate the slope f (3.5) for f(x)-sin(3xusing: a. Forward difference approximation...
use radians in trig
functions
Estimate the slope f (3.5) for f(x)-sin(3xusing: a. Forward difference approximation with h 0.2 b. Backward difference approximation with h 0.2 c. Centered difference approximation with h 0.2. For each estimated slope, provide the true percent relative error, & Which approximation is the most accurate? Box your answ ers
Compute the backward and center difference approximations for the 1st derivative of y = log x...
Compute the backward and center difference approximations for the 1st derivative of y = log x evaluated @ x=20 and h=2. Using the second order error O(h2) formula.
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first...
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first derivative using, 2, 3, and 4 points for the function y = cos x at x = 7/4 using step size h = /12. Provide the results in the hard copy. Note that the central differences can only be apply for odd number of points ). b. Provide the analytic form of the derivatives, as well as table of the computed relative error for...
Numeric Analysis 1) Letf(x)=- 2x x2-4 a. Approxi the first derivative using central difference and the...
Numeric Analysis
1) Letf(x)=- 2x x2-4 a. Approxi the first derivative using central difference and the second derivative mate at x= 1.25 using and h=0.25. (Use 4 decimal digits using backward difference rounding). Approximate f f(x)dx using trapezoidal rule with h-0.5 (Use four decimal digits rounding) c. Approximate S fCx)dxusing 1/3 Simpson's rule with h-0.25 (Use four decimal digits rounding)
#7. [Extra Credit] is calculus wrong?! Consider f(x) = ex (a) Calculate the derivative of fx) atx...
#7. [Extra Credit] is calculus wrong?! Consider f(x) = ex (a) Calculate the derivative of fx) atx 0 using O(h) finite difference (forward and backward) and O(h2) centered finite difference. Vary h in the following manner: 1, 101,102... 1015. (Write a MATLAB script for this purpose and call it pset5_prob7) (b) Modify your script to plot (log-log) the the true percent error in all three cases as a function of h in one plot. (c) In calculus we learned that...
Problem statement: Use forward and backward difference approximations of 0(h) and a centered difference approximation of...
Problem statement: Use forward and backward difference approximations of 0(h) and a centered difference approximation of 0(h') to estimate the first derivative of f(x)- 0.x-0.15x-0.5x-0.25x +12 Problem #2 Steady-state temperatures (K) at three nodal points of a long rectangular rod as shown. The rod experiences a uniform volumetric generation rate of 5 X 10 Wm and has a thermal conductivity of 20 W/m-K. Two of its sides are maintained at a constant temperature of 300K, while others are insulated. Problem...
2. Use the notation in this section, derive the centered difference approxima- tion to the first derivative, u(x +h)-u (x-h) u,(x) + O(h2) = 2h 2. Use the notation in this section, derive th...
2. Use the notation in this section, derive the centered difference approxima- tion to the first derivative, u(x +h)-u (x-h) u,(x) + O(h2) = 2h
2. Use the notation in this section, derive the centered difference approxima- tion to the first derivative, u(x +h)-u (x-h) u,(x) + O(h2) = 2h
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...
use radians in trig
functions
Estimate the slope f (3.5) for f(x)-sin(3xusing: a. Forward difference approximation with h 0.2 b. Backward difference approximation with h 0.2 c. Centered difference approximation with h 0.2. For each estimated slope, provide the true percent relative error, & Which approximation is the most accurate? Box your answ ers
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first derivative using, 2, 3, and 4 points for the function y = cos x at x = 7/4 using step size h = /12. Provide the results in the hard copy. Note that the central differences can only be apply for odd number of points ). b. Provide the analytic form of the derivatives, as well as table of the computed relative error for...
Numeric Analysis
1) Letf(x)=- 2x x2-4 a. Approxi the first derivative using central difference and the second derivative mate at x= 1.25 using and h=0.25. (Use 4 decimal digits using backward difference rounding). Approximate f f(x)dx using trapezoidal rule with h-0.5 (Use four decimal digits rounding) c. Approximate S fCx)dxusing 1/3 Simpson's rule with h-0.25 (Use four decimal digits rounding)
#7. [Extra Credit] is calculus wrong?! Consider f(x) = ex (a) Calculate the derivative of fx) atx 0 using O(h) finite difference (forward and backward) and O(h2) centered finite difference. Vary h in the following manner: 1, 101,102... 1015. (Write a MATLAB script for this purpose and call it pset5_prob7) (b) Modify your script to plot (log-log) the the true percent error in all three cases as a function of h in one plot. (c) In calculus we learned that...
Problem statement: Use forward and backward difference approximations of 0(h) and a centered difference approximation of 0(h') to estimate the first derivative of f(x)- 0.x-0.15x-0.5x-0.25x +12 Problem #2 Steady-state temperatures (K) at three nodal points of a long rectangular rod as shown. The rod experiences a uniform volumetric generation rate of 5 X 10 Wm and has a thermal conductivity of 20 W/m-K. Two of its sides are maintained at a constant temperature of 300K, while others are insulated. Problem...
2. Use the notation in this section, derive the centered difference approxima- tion to the first derivative, u(x +h)-u (x-h) u,(x) + O(h2) = 2h
2. Use the notation in this section, derive the centered difference approxima- tion to the first derivative, u(x +h)-u (x-h) u,(x) + O(h2) = 2h
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