Numerical Analysis
Consider the same five-data pair (x, y) and-
Find the first and second derivatives exactly at x = c. (c is any x in your data!)- Obtain the three-point forward difference formula for the second order derivative with a remainder by using the Taylor series expansion. Calculate f¢¢(c) by using this formula for the data given.- Obtain the three-point backward difference formula for the second order derivative with a remainder by using the Taylor series expansion. Calculate f¢¢(c) by using this formula for the data given.- Obtain the three-point central difference formula for the second order derivative with a remainder by using the Taylor series expansion. Calculate f¢¢(c) by using this formula for the data given.
You can choose any five data pair.
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Use the Taylor expansion to derive three finite difference schemes (forward-difference, backward-...
Use the Taylor expansion to derive three finite difference schemes (forward-difference, backward- difference and central-difference) of the first derivatives as well as the central difference scheme of the second derivative and comment on the accuracy order of each scheme. [10%]
Use the Taylor expansion to derive three finite difference schemes (forward-difference, backward- difference and central-difference) of the first derivatives as well as the central difference scheme of the second derivative and comment on the accuracy order of each scheme. [10%]
11.3 Concepts: Error Order and Precision pts The following is a 5-point backward difference schem...
Here is 11.1 for reference. I need help with 11.3
11.3 Concepts: Error Order and Precision pts The following is a 5-point backward difference scheme, over equally-spaced x, for df/dx at xx 25/,-48f-+36f-2-16-3+34 12 Ar Write out Taylor Series expressions for each of the four fa, f f fto the SIXTH derivative, like you did in 11.1, and then combine them using the difference scheme above to a) Calculate the discretization error order (i.e. write the erro(Ax) for some integer...
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.
Most of practical problems in engineering involve functions of several independent variables as t...
Most of practical problems in engineering involve functions of several independent variables as thermal, strain and stress are multidimensional and transient such Two-point backward first order derivative is given Two-point central difference is given by Two-point forward difference is given by Three-point Second order partial derivative central difference is given by The second-order mixed four-point central finite difference is given by (x Convert the boundaries derivatives to second accuracy scheme The vorticity is given by The shear stress is given...
Need ASAP Please !!!!!!! Write user defined MATLAB code for the following question. for all 3...
Need ASAP Please !!!!!!!
Write user defined MATLAB code for the following question. for all 3 parts a, b and c. Given the following data: x 0.6 0.7 0.8 0.9 1. fx) 5.2296 3.61552.7531 2.2717 2 find the second derivative f"(x) at the point x = 0.8. (a) Use the three-point forward difference formula. (b) Use the three-point backward difference formula. (c) Use the three-point central difference formula.
3. For f(x) = e-x and h = 0.6
3. For f(x) = e-x and h = 0.6 a) Use forward and backward difference approximations to estimate the second derivatives of f(x) at x = 2. Use the least accurate formulas available.b) Using the most accurate centered difference formula, estimate the second derivative of f(x) at x=2.
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered approximations to estimate the first and second derivatives of f(x) at x = 2. Use the east accurate formulas available. (10 pts) b) Using the most acurate forward and backward difference formulas, estimate the first derivative of f(x) at x 2. (10 pts) Forward Difference First Derivative 7.) - SD Error OM or) = -1.) + 40..) - 3 ) 2h Second Derivative 'w...
Calculate the first nonzero term in the Taylor series of the truncation error Tr(h) for the...
Calculate the first nonzero term in the Taylor series of the truncation error Tr(h) for the finite difference formula defined by the second row of Table 5.2. Table 5.2. Weights for forward finite difference formulas (p 0 in (5.4.2). The values given here are for approximating the derivative at zero. See the text about the analogous backward differences where q=0. The term order of accuracy is explained in Section 5.5. Order of Node location 2h 3h 4h accuracy 1 2...
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...
Please help me answer this question using matlab Consider the function f(x) x3 2x4 on the...
Please help me answer this question using matlab
Consider the function f(x) x3 2x4 on the interval [-2, 2] with h 0.25. Use the forward, backward, and centered finite difference approximations for the first and second derivatives so as to graphically illustrate which approximation is most accurate. Graph all three first-derivative finite difference approximations along with the theoretical, and do the same for the second derivative as well
Use the Taylor expansion to derive three finite difference schemes (forward-difference, backward- difference and central-difference) of the first derivatives as well as the central difference scheme of the second derivative and comment on the accuracy order of each scheme. [10%]
Use the Taylor expansion to derive three finite difference schemes (forward-difference, backward- difference and central-difference) of the first derivatives as well as the central difference scheme of the second derivative and comment on the accuracy order of each scheme. [10%]
Here is 11.1 for reference. I need help with 11.3
11.3 Concepts: Error Order and Precision pts The following is a 5-point backward difference scheme, over equally-spaced x, for df/dx at xx 25/,-48f-+36f-2-16-3+34 12 Ar Write out Taylor Series expressions for each of the four fa, f f fto the SIXTH derivative, like you did in 11.1, and then combine them using the difference scheme above to a) Calculate the discretization error order (i.e. write the erro(Ax) for some integer...
Most of practical problems in engineering involve functions of several independent variables as thermal, strain and stress are multidimensional and transient such Two-point backward first order derivative is given Two-point central difference is given by Two-point forward difference is given by Three-point Second order partial derivative central difference is given by The second-order mixed four-point central finite difference is given by (x Convert the boundaries derivatives to second accuracy scheme The vorticity is given by The shear stress is given...
Need ASAP Please !!!!!!!
Write user defined MATLAB code for the following question. for all 3 parts a, b and c. Given the following data: x 0.6 0.7 0.8 0.9 1. fx) 5.2296 3.61552.7531 2.2717 2 find the second derivative f"(x) at the point x = 0.8. (a) Use the three-point forward difference formula. (b) Use the three-point backward difference formula. (c) Use the three-point central difference formula.
3. For f(x) = e-x and h = 0.6 a) Use forward and backward difference approximations to estimate the second derivatives of f(x) at x = 2. Use the least accurate formulas available.b) Using the most accurate centered difference formula, estimate the second derivative of f(x) at x=2.
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered approximations to estimate the first and second derivatives of f(x) at x = 2. Use the east accurate formulas available. (10 pts) b) Using the most acurate forward and backward difference formulas, estimate the first derivative of f(x) at x 2. (10 pts) Forward Difference First Derivative 7.) - SD Error OM or) = -1.) + 40..) - 3 ) 2h Second Derivative 'w...
Calculate the first nonzero term in the Taylor series of the truncation error Tr(h) for the finite difference formula defined by the second row of Table 5.2. Table 5.2. Weights for forward finite difference formulas (p 0 in (5.4.2). The values given here are for approximating the derivative at zero. See the text about the analogous backward differences where q=0. The term order of accuracy is explained in Section 5.5. Order of Node location 2h 3h 4h accuracy 1 2...
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 help me answer this question using matlab
Consider the function f(x) x3 2x4 on the interval [-2, 2] with h 0.25. Use the forward, backward, and centered finite difference approximations for the first and second derivatives so as to graphically illustrate which approximation is most accurate. Graph all three first-derivative finite difference approximations along with the theoretical, and do the same for the second derivative as well
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