Write down the formula for the euler method

Assignment Help MATLAB Programming
Reference no: EM133055914

FD methods of ODEs

Question 1. Apply Euler Method with step size h = 1/10 to find the approximate solution for the initial value problem:

y' = 5t4y, t ∈(0, 1]
y(0) = 1

(a) Show that the exact solution is: y = y(t) = et5.
(b) Write down the formula for the Euler Method and provide with the Matlab programs by the method.
(c) Plot the approximate solutions given by the Euler Methods on [0, 1] with step size h = 0.1 along with the exact solution.
(d) Provide with a table of the t values, approximations, and global trun- cation errors of the approximate solutions over the points, t0, t1, t2.

Question 2. Apply the second-order Taylor Method to the initial value problems in Exercise 1. Using step size h = 1/4, calculate the approximation on the interval [0, 1]. Compare with the correct solution and find the error at t = 1.

Question 3. Use the the Heun Method to solve the IVP: y' = t2y,   y(0) = 1 with t ∈ [0, 1] and the exact solution: y = et3/3.

(a) Plot the global truncation error of the Heun Method at t = 1 as a function of h = 0.1 2-k for 0 k 5 and compute the numerical convergence orders.

(b) Plot the Heun Method approximate solution on [0, 1], along with the exact solution. Use the step sizes h = 0.1.

Question 4. Apply Runge-Kutta method of order 4 to the IVP in Exercise 1. Give the general formula of the RK4 method and the Matlab codes. Print a table of the t variable values, approximations and global truncation error at each step on a grid of step size h = 0.1. Plot the approximate solutions for the step sizes h = 0.1 along with the exact solution.

Reference no: EM133055914

Questions Cloud

What is your total profit or loss to date : Futures contracts on gold are based on 75 tory ounces and priced in dollars per tory ounce. Assume the February gold contract settled today at 1365.10 and opene
What is adm effective price per bushel for transaction : ADM purchases 55,000 bushels of soybeans in July. In January, when the spot price of soybeans was $10.50/bushel, ADM hedged the entire planned purchase with Sep
How many months will it take before he pays off the card : If he makes the minimum payment and makes no other charges, how many months will it take before he pays off the card
How much overhead would be allocated to the period : If the actual direct labor hours for the period are 350,000, how much overhead would be allocated to the period
Write down the formula for the euler method : Write down the formula for the Euler Method and provide with the Matlab programs by the method and Plot the approximate solutions given by the Euler Methods
Modern day operating systems : Describe, compare, and contrast the security features that are in today's modern day operating systems.
Determine the budgeted purchases of Product A : Beginning inventory for the current month is 3,600 units, Determine the budgeted purchases of Product A for the current month
Allocate the building-related costs : Would you recommend that TRU continue to allocate the building-related costs only to the preschool program? What alternative allocation method would you suggest
What is false discovery rate : The concept of false discovery in data. After reviewing the article by Naouma (2019), What is a false discovery rate?

Reviews

Write a Review

MATLAB Programming Questions & Answers

  Finite difference method

Use the finite difference method to calculate the temperature at the point specified since it is easier.

  Determine the necessary shell temperature

In a shell-and-tube heat exchanger, one fluid passes through a central tube while another fluid flows through an outer shell in the opposite direction. The purpose is to heat the fluid passing through the central tube.

  Find the integral of a function at an arbitrary location

Write a Matlab function to perform numerical integration of a set of evenly spaced data points using the trapezoidal rule

  Compute the speed of single-stage planetary gear train

Write a MATLAB function [speed] = planetary (N, emesh, first, last, arm) that computes the speed of a given link in a single-stage planetary gear train.

  Calculate and plot the error in the numerical derivative

Write a program to calculate and plot the error in the numerical estimate of the derivative.

  Create the graph using matlab functions

Create the graph, which contains a piecewise function where a line exists in the first interval, a parabola in the second interval, and the sine function in the third interval.

  Develop a simulation program

Develop a simulation program

  Create a vector in matlab

Create a three dimensional diagram of function.

  Open a named pipe and to read data from the pipe

Open a named pipe and to read data from the pipe in matlab

  Write the commands that will create the matrix

Write the commands that will create the matrix.

  Lagrange interpolating polynomial of degree

Lagrange interpolating polynomial of degree

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd