M3G124711 - Advanced Mathematics for Civil Engineers - Knowledge of Numerical Integration - Gauss Seidel Method - Boundary Conditions - Mathematics Assignment Help

Assignment Task :

Aim  To assess learning emphasized on the development of students’ ability to use numerical techniques for the problems in engineering and science whose solution is either difficult or impossible using classical techniques.
 

Learning Outcomes
1. Get the knowledge of numerical integration for applications. Simpson’s rule
2. Solve ordinary differential equations numerically using Euler’s method, RK-2 and RK-4.
3. Solve partial differential equations numerically using finite difference method.

Task(s)
Students are expected to solve assignment questions with the acquired knowledge from class room lectures, tutorial sessions and by referring CCE learn postings, indicative reading and ebrary resources and e-resources indicated at the end of the assignment questions individually.

Q1Approximate the positive root of the equation x2 - sin x - 1 = 0 , by performing five iterations of the following methods, with 5-digits rounding:

(a)Bisection method

(b)Newton-Raphson method

(c)Fixed-point method with the test for convergence.

Q2Find the solution to the following system of linear equations with 4-digts rounding, using:

(a)Gauss elimination

(b)Gauss-Seidel method (performing three iterations)
4x - y = 3, 5y - 3z = 0, x + 2y - 6z = 1

Q5 Solve the following problem in the given domain by

(i) Euler’s method

(ii) RK-2 , using4- digits rounding.

Compare your results with the given exact solution. Graph the exact solution and the solution by Euler’s method and RK-2 (connecting values of y by the straight line segments.

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