+61-413 786 465

[email protected]

 Algebra Math Calculus Physics Chemistry Biology Earth Science Physiology History Humanities English Sociology Nursing Science

Home >> Math

Instructions

The aim of the assignment is that the student/group studies and applies numerical methods such as Euler's method, the Improved Euler's method and the Runge-Kutta method to solve first-order differential equations numerically. The main reference is Section 1.7 of the textbook "Notes on diffy Qs differential equations for engineers" by Lebl. The improved Euler's method is explained after Exercise 1.7.103 and the Runge-Kutta method is explained after Exercise 1.7.6. The assignment has a value of 53 points, and it is worth 15% of the total marks of the course. It consists of two parts: a powerpoint presentation and two exercises to be solved. The assignment is meant to completed by groups or individually. Students are encouraged to
join a group.

PowerPoint presentation

The student/group should create a PowerPoint presentation of up to eleven slides explaining the main ideas behind Euler's method, the Improved Euler's method and the Runge-Kutta method. The presentation should be clear enough so that any student from the class can understand its elements. It should explain the following topics for each method.

(1) Geometric reason behind the corresponding method. A graph should be presented (for each method).

(2) A clear explanation of the method, which should include one example. Use the same example for the three methods.

(3) A table comparing the numerical values of the three methods, as in the table below.

 xn yn Euler Improved Euler Runge-Kutta

Exercises

The marks are computed as follows: 5 points for the exact solution, 3 5 points for the formulas and workings for h = 0.1, 5 points for the h = 0.1 table, and 5 points for the Excel spreadsheet.

Each student/group will solve two of the following four exercises. The solution of each ex- ercise should again be clear enough so that any student from the class can understand its basic elements. The assignment could be handwritten. Just make sure that your writing is clear.

Statement. Use Euler's method, the Improved Euler's method and the Runge-Kutta method to obtain a four-decimal approximation of the indicated value for two of the exercises below.

(1) For each method use h = 0.1.

(2) Provide the exact solution of each exercise.

(3) For each method, you need to provide the relevant formulas and workings to obtain the five xn and yn for h = 0.1. This part should be done manually.

(4) After running each method, provide a table as the one below.
Recall that the error is the difference between the actual solution and the approximate solution.

(5) The numerical solutions of each exercise should be implemented in Excel but for h = 0.01. Attach a copy of one Excel spreadsheet which follows the format of the table.

Table 1. Comparison of numerical methods with h = 0.1

 xn yn Euler Improved Euler Runge-Kutta Exact Value Error

Ex 1.: yj = 2x 3y + 1, y(1) = 5; y(1.5).
Ex 2.: yj = e-y, y(0) = 0; y(0.5). (This is a separable equation)
Ex 3.: yj = 2xy, y(1) = 1; y(1.5). (This is a separable equation)
Ex 4.: yj = y - y2, y(0) = 0.5; y(0.5). (This is a separable equation) The method for selecting the exercises is the following.

(1) In a group, select the person whose surname comes first in alphabetical order, out of the surnames of the group members. If there is only one student, select his/her surname.

(2) Obtain the position of the first letter of the surname in the English alphabet. For instance, a surname starting with D has position 4, while a surname starting with F has position 6.

(3) To select the two exercises from the four exercises given above, obtain the remainder r of the integer division of the position of the surname and 3. For instance, 4 divided by 3 has remainder r = 1 and 5 has remainder r = 2. Solve the exercises r + 1 and r + 2. That is, if the remainder is r = 2, you should solve the exercises 3 and 4.

• Category:- Math
• Reference No.:- M93136015
• Price:- \$55

Guranteed 36 Hours Delivery, In Price:- \$55

Have any Question?

## Related Questions in Math

### Question 1 - for the ivp of ode y t-1e-y y1 0 find an

Question 1 - For the I.V.P of ODE y' = (t-1)e -y , y(1) = 0, find an approximation to y(1.2) using the following numerical methods with Δt = 0.1. Compare the numerical solution with the exact solution and compute the err ...

### Assessment taskpractical investigation- question 1 requires

Assessment Task Practical Investigation - Question 1 requires selecting reference points from the graph. It is expected that each student will choose different reference points to other students. Take note of the criteri ...

### Instructionsthe aim of the assignment is that the

Instructions The aim of the assignment is that the student/group studies and applies numerical methods such as Euler's method, the Improved Euler's method and the Runge-Kutta method to solve first-order differential equa ...

### Assignment - solving the five question in the very details

Assignment - Solving the five question in the very details, thanks a lot. Question - Let a ∈ P n be a point. Show that the one-point set {a} is a projective variety, and compute explicit generators for the ideal I p ({a} ...

### Maths assignment - 1 analysis of a data setusing a

Maths Assignment - 1. Analysis of a data set Using a continuous data set you are requested to collect in the types of data and gathering data section, perform a statistical analysis on your data. You have opportunities t ...

### 1 suppose that n 10088821 is a product of two distinct

1. Suppose that n = 10088821 is a product of two distinct primes, and Φ(n) = 10082272. Determine the prime factors of n. 2. It is easy to show that the converse of Fermat's Theorem does not hold; i.e., the congruence a n ...

### Mathematics- algebraic geometry problemlet k denotes an

Mathematics- Algebraic Geometry Problem Let K denotes an algebraically closed field and let P 1 be constructed as in Example 5.5(a) in Gathmanns notes, i.e. P 1 is the gluing of X 1 = A 1 and X 2 = A 1 along  the open su ...

### Assignment -question 1 let t and or 0 1 be a boolean

Assignment - Question 1. Let (T, ∧, ∨,', 0, 1) be a Boolean Algebra. Define ∗ : T × T → T and o : T × T → T as follows: x ∗ y := (x ∨ y)' x o y := (x ∧ y)' (a) Show, using the laws of Boolean Algebra, how to define x ∗ y ...

### Mathematics- algebraic geometry problemlet k denotes an

Mathematics- Algebraic Geometry Problem Let K denotes an algebraically closed field and let P 1 be constructed as in Example 5.5(a) in Gathmanns notes, i.e. P 1 is the gluing of X 1 = A 1 and X 2 = A 1 along  the open su ...

### Question 1 what is the nth order approximation using taylor

Question: 1. What is the nth order approximation using Taylor series? 2. What is Error Propagation? 3. Please explain what the total numerical error is? Please illustrate how the change of step size will affect the total ...

• 13,132 Experts

## Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

### Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

### Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

### Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of \$ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

### Compute the present value of an 1150 payment made in ten

Compute the present value of an \$1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

### Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of \$ 699 per year for 19 years, given a discount rate of 6 percent per annum. As