Question: Derive the 2nd order finite difference approximation of f(x) () using Taylor series expansion. [2 marks] Discuss the order truncation error of finite difference

Derive the 2nd order finite difference approximation of f(x) () using Taylor

Derive the 2nd order finite difference approximation of f(x) () using Taylor series expansion. [2 marks] Discuss the order truncation error of finite difference approximations. Include how the order of truncation error effect the error when halving the step size h. [4 marks]

Step by Step Solution

★★★★★

3.51 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To derive the secondorder finite difference approximation of fx we can use the Taylor series expansi... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Finance Questions!

In Exercises use the shell method to find the volume of the solid generated by revolving the plane region about the given line. y = x, y = 4x - x, about the line x = 4

Create an application using PyQt. The user is prompted for the name of an animal rescue service. This must be displayed in the UI in capital letters. The user is then required to enter a character...

Assuming that the directors decide to declare total dividends in the amount of $393,900, determine how much each class of shares should receive if the preferred shares are non-cumulative and are...

3. Finley Heaters Inc. is a mid-sized manufacturer of residential water heaters. Sales have grown during the last several years, and the company's production capacity needs to be increased. The...

1An average American consumes approximately 10 6 kJ of energy per day. The average life expectancy of an American is 77.9 years. If it takes2.6109g2.6109of coal to meet a person's energy demands per...

Need solutions for solving 4.4 and 4.8 using python. Questions are attached as a screenshot. and a centered dallerence approximation o O) to estimate the first derivative of the function examined in...

close all;clear all;clc %Construct vector with varying values of h h=[0.1 0.01 0.001]; %Determine the number of elements in h nh=length(h); for ii=1:nh %construct a set of equally spaced...

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

1 (Graded). (i) Determine the exact solution to the IVP y' = siWy 11(1) = 2 (ii) Implement the 4stage RungeKutta method given by the Butcher tableau Test it on the IVP from (i J on the interval I [1...

Example 3.36. Consider the IVP (3.88) y' =y y(0) =1 We know that the exact solution is y(x) = e". Let us run Euler's method, say on the interval [0, 1]: (3.89) Un+1 = Un + hF(In, y(x.)) (3.90) Un+1 =...

You own a portfolio that is 35 percent invested in Stock X, 20 percent in Stock Y, and 45 percent in Stock Z. The expected returns on these three stocks are 9 percent, 17 percent, and 13 percent,...

Pictograph assignment . You must Illustrate the following text: Drink your first glass of water when you wake up in the morning. Drink your second glass of water at noon before you eat lunch. And...

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A . lim h 0 4 9 h - 4 9 h = B . The limit does not exist and is neither nor - .

The following transactions took place in December 2017 for MegaMart. MegaMart uses the contract- based approach to revenue recognition and a perpetual inventory system. MegaMart estimates returns at...

When birth weights were recorded for a simple random sample of 16 male babies born to mothers taking a special vitamin supplement, the sample had a mean of 3.675 kilograms and a standard deviation of...

Beacon Company maintains and repairs warning lights, such as those found on radio towers and lighthouses. Beacon Company prepared the end-of-period spreadsheet shown on below at October 31, 2012, the...

Thames Garden Supplies uses a perpetual inventory system. Thames Garden Supplies has these account balances at July 31, 2010, prior to making the year-end adjustments: A year ago, the replacement...

Communication is most critical elements of a firm. Discuss about the communication process at BoldFlash Company. Address the following: 1. Outline a written report or a training video (or both) in...

Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.34ex dx,0 n =6

Please derive the 2nd order irreversible equation for a plug flow reactor Second-order, irreversible reaction, A+B products with equimolar feed or 2A products, any constant A,...

2. Cylindrical Muscle. A cylindrical muscle of radius b is excised from the animal and is hung in a physiological solution. The partial pressure of O2 in the solution is Po. Assume zero-order...

Convert the given 2nd order nonlinear PDE into a finite set of ODES Using Galerkin method D[u(x)] = -(x,t) + u"(x,t) + qu(xt)=0 (1) a2u here, (x,t)= at2 and u"(x,t)= axi 02u 2 Boundary conditions are...

Each question is correlated to the previous question, so please answer all. Thanks! 1) Derive the equations for solving system of linear equations using pivoting along the lines of the notes or the...

Problem Statement Sydney Food Festival (SFF) is an annual event that happens in the month of June and it runs for a week. The festival showcases Sydney's best food, prepared fresh in food trucks for...

%% Finite Difference (FD) computation loop % Important: Other parameters may not be mentioned here, % and you might need to define them. xm = 80; %km dx = 1; %km dt = 0.2; %s B = 2; %km/s sd = 4; %s...