Explain why the local discretization error of the finite difference method is proportional to the square of

Question:

Explain why the local discretization error of the finite difference method is proportional to the square of the step size. Also explain why the global discretization error is proportional to the step size itself.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Heat And Mass Transfer Fundamentals And Applications

ISBN: 9780073398181

5th Edition

Authors: Yunus Cengel, Afshin Ghajar

See More Books

Question Posted: Sep 16, 2023 06:48 AM

See More Questions

We will investigate the local discretization error in applying the Euler approximation given by equations (5) and (6). (a) If y(t) is the exact solution of y' = f(t. y) use the chain rule to...
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
This case was written by Professor Michele Greenwald, Visiting Professor of Marketing at HEC Paris, for use with Advertising and Promotion: An Integrated Marketing Communications Perspective 7th...
Repeat Prob. 37 using singularity functions exclusively (including reactions). Repeat Prob. 37, For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment...
In 2009, BMJ Plumbing Company sold 400 water heaters for $350 each. The water heaters carry a two-year warranty for repairs. BMJ Plumbing estimates that repair costs will average 2 percent of the...
Frank Willingham has the following transactions during the year: Sale of office equipment on March 15 that cost $20,000 when purchased on July 1, 2012. Frank has claimed $5,000 in depreciation and...
Show that, for irrotational axisymmetric flows in cylindrical coordinates, the streamfunction satisfies the following equation: \[\frac{\partial^{2} \psi}{\partial r^{2}}-\frac{1}{r}...
A truck with a cost of $82,000 has an estimated residual value of $16,000, has an estimated useful life of 12 years, and is depreciated by the straight-line method. (a) Determine the amount of the...
As part of the marketing team for a new ice cream manufacturer, develop a consumer sales promotion and trade sales promotion plan for your product. Use at least two consumer sales promotion and two...
International Foods, a U.S. company, acquired two companies in 2013. As a result, its consolidated financial statements include the following acquired intangibles: Goodwill was assigned to the...
What causes the round-off error? What kind of calculations are most susceptible to round-off error?
How is the finite difference formulation for the first derivative related to the Taylor series expansion of the solution function?
Use regression analysis to fit a quadratic trend model to the data set. a. What is the estimated regression function? b. Compare the adjusted-R2 value for this model to that of the linear trend...
Some brokers (called viatical brokers) offer cash settlements in advance to people with terminal diseases who have life insurance, paying them in advance of their death. Is this practice ethical? Is...
R. Kennedy is a security van driver. He has a wage of 200 per week, plus danger money of 2 per hour extra spent in transporting gold bullion. During the week ended 15 June 2012 he spends 20 hours...
A company maintains its non-current assets at cost. Depreciation provision accounts for each asset are kept. At 31 December 2011 the position was as follows: The following additions were made during...
Describe the aspects of health that make it a consumption good. Describe those that make it an investment good.
The deductible feature of an insurance policy can affect the impact of moral hazard. Explain this in the context either of probability of treatment and/or amount of treatment demanded.
Bostick Co. acquired the assets of Belk Co. for $1,200,000 in 2016. The estimated fair market value of the assets at the acquisition date was $1,000,000. Goodwill of $200,000 was recorded at...
Thalina Mineral Works is one of the worlds leading producers of cultured pearls. The companys condensed statement of cash flows for the years 20182020 follows. Required Comment on Thalina Mineral...
Repeat Prob. 5134E when the supply line carries oxygen at 300 psia and 450F. Data From Q#134: The weighted piston of the device shown in Fig. P5134E maintains the pressure of the piston-cylinder...
The weighted piston of the device shown in Fig. P5134E maintains the pressure of the piston-cylinder contents at 200 psia. Initially, this system contains no mass. The valve is now opened, and steam...
The air in an insulated, rigid compressed-air tank whose volume is 0.5 m 3 is initially at 2400 kPa and 20C. Enough air is now released from the tank to reduce the pressure to 2000 kPa. Following...
paid $ 8 2 on January 2 2 0 2 4 , for 2 shares of Came Cosmetics common stock The investment represents a 2 0 % interest in the net assets of Came and gave the ability to exercise significant...
Complete the following, determining the appropriate uncertainty: ( a ) ( 2 . 7 0 \ pm 0 . 0 5 cm ) 2 ( b ) ( 2 . 7 0 \ pm 0 . 0 7 cm ) 3 ( c ) ( 1 2 . 0 2 \ pm 0 . 0 8 cm ) 4 ( d ) ( 2 0 . 6 ...
Given f and g, find (a) fog(x) and its domain, and (b)gof(x) and its domain. f(x) = x+2, g(x) = x + x-4 ==

Explain why the local discretization error of the finite difference method is proportional to the square of

Question:

Step by Step Answer:

The finite difference method is a numerical technique used to approximate the derivatives of a function When using this method you discretize a contin...View the full answer

Heat And Mass Transfer Fundamentals And Applications

Students also viewed these Engineering questions