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Subject

Numerical Method

This course contains the concepts of numerical method techniques for solving linear and nonlinear equations, interpolation and regression, differentiation and integration, and partial differential equations. The main objective of the course is to provide the knowledge of numerical method techniques for mathematical modeling.

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solve the Poisson’s equation ∇²f = xy and f=2 on boundary by assuming square domain 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3 and h=1.

Not Answered Numerical Method

What is differential equation? Differentiate between ODE and PDE with example.

Not Answered Numerical Method Asked on 2081 Exam

Solve the Poisson equation
\[
\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = -64xy, \quad 0 \leq x \leq 1,\; 0 \leq y \leq 1
\]
with boundary conditions:
\[
u(0, y) = 0,\quad u(x, 0) = 0,\quad u(1, y) = 150,\quad u(x, 1) = 150 \quad \text{and} \quad h = \frac{1}{3}.
\]

Not Answered Numerical Method Asked on 2081 Exam

Solve \(\frac{dy}{dx} = \frac{x}{y}, \quad y(0) = 1\), at \(x = 0.4\) using Runge–Kutta’s \(4^{\text{th}}\) order method.

Not Answered Numerical Method Asked on 2081 Exam

Given the data points below

X 1.0 3.0 4.0

f(x) 1.5 4.5 9.0

Find cubic spline which belongs to 1<=x<=3 and estimate f(2) using cubic splines.

Not Answered Numerical Method Asked on 2081 Exam

Solve the following system of linear equations using Gauss-Jordan elimination method.

x+2y-3z=4

2x+4y-6z=8

x-2y+5z=4

Not Answered Numerical Method Asked on 2081 Exam

What is an application of numerical integration? Find the value of the integral
\[
\int_1^2 \frac{e^x}{x} \, dx
\]
using Simpson’s \( \frac{3}{8} \) rule with \( n = 6 \).

Not Answered Numerical Method Asked on 2081 Exam

What is numerical differentiation? The table below gives the values of distance travelled by a vehicle at various time interval, estimate the velocity and acceleration at x = 4.

Time(x) 1 2 4 8 10

Distance(y) 0 1 5 21 27

Not Answered Numerical Method Asked on 2081 Exam

What is regression analysis? Fit a second order polynomial for the following data values.

x 2 4 6 8 10

y 1.4 2.0 2.4 2.6 2.8

Not Answered Numerical Method Asked on 2081 Exam

Consider the following data points estimate the f(0.6) using Newton’s interpolation formula.

x 0.1 0.2 0.3 0.4 0.5

f(x) 2.68 3.04 3.38 3.69 3.97

Not Answered Numerical Method Asked on 2081 Exam

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