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BCA Semester 4 – Numerical Methods – Unit 5: Solution of Ordinary Differential Equations (7Hrs.)

Comprehensive questions and detailed answers for Unit 5: Solution of Ordinary Differential Equations (7Hrs.). Perfect for exam preparation and concept clarity.

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1

Use the classical RK method to estimate y(0.4) of the equation

\quad \quad \frac{dy}{dx}=x^2+y^2

with y(0)=0, assume $h=0.2$ .

MediumTHEORY5 marks2021(TU FOHSS Final)

2

Prepare the multi-step methods available for solving ordinary differential equations. Evaluate the value of y at $x = 0.1$ and $0.2$ to 4 decimal places given

\frac{dy}{dx}=x2y−1,\quad y(0)=1,

using Taylor series method.

MediumTHEORY10 marks2022(TU FOHSS Final)

3

Define ordinary differential equation. Use the fourth order Runge-Kutta method to estimate $y(0.4)$ of the equation:

\quad \quad \frac{dy}{dx}=x2+y2

with $y(0) = 0$ assuming that $h = 0.2$

MediumTHEORY5 marks2023(TU FOHSS Final)

4

a) Write and implement an algorithm to solve the system of linear equations using Gauss-Seidel method with suitable example
b) Write and implement an algorithm to solve the ODE using Heun's method.

MediumTHEORY10 marks2023(TU FOHSS Final)

5

Using Runge-Kutta method of 4th order solve the following equation taking each step $h = 0.1$

\quad \quad \quad \frac{dy}{dx}=4xy - xy

given $y(0) = 3.3$ calculate y at $x = 0.1\space and\space 0.2.$

MediumTHEORY5 marks2024(TU FOHSS Final)

6

Define initial value problems and final value problems. Using heun’s method, find value of y when $x=0.3$ given that

\quad \quad \frac{dy}{dx} = x + y \space and \space y=1

when $x=0$ .

MediumTHEORY10 marks2024(TU FOHSS Final)

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Sample Questions

Use the classical RK method to estimate y(0.4) of the equation \[ \quad \quad \frac{dy}{dx}=x^2+y^2 \] with y(0)=0, assume \(h=0.2\).

Marks: 5Chapter: Unit 5: Solution of Ordinary Differential Equations (7Hrs.)

Prepare the multi-step methods available for solving ordinary differential equations. Evaluate the value of y at \(x = 0.1\) and \(0.2\) to 4 decimal places given \[\frac{dy}{dx}=x2y−1,\quad y(0)=1,\]

Marks: 10Chapter: Unit 5: Solution of Ordinary Differential Equations (7Hrs.)

Define ordinary differential equation. Use the fourth order Runge-Kutta method to estimate \(y(0.4)\) of the equation: \[ \quad \quad \frac{dy}{dx}=x2+y2 \] with \(y(0) = 0\) assuming that \(h = 0.2\

Marks: 5Chapter: Unit 5: Solution of Ordinary Differential Equations (7Hrs.)

a) Write and implement an algorithm to solve the system of linear equations using Gauss-Seidel method with suitable example\ b) Write and implement an algorithm to solve the ODE using Heun's method.

Marks: 10Chapter: Unit 5: Solution of Ordinary Differential Equations (7Hrs.)

Using Runge-Kutta method of 4th order solve the following equation taking each step \( h = 0.1\) \[\quad \quad \quad \frac{dy}{dx}=4xy - xy \] given \(y(0) = 3.3\) calculate y at \(x = 0.1\space and\

Marks: 5Chapter: Unit 5: Solution of Ordinary Differential Equations (7Hrs.)

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