PYQs

1) Use Euler’s method with step size h=0.15 to compute the approximate value of y(0.6), correct up to five decimal places from the initial value problem, where y′=x(y+x)−1, y(0)=2.

[2013, 15M]

2) Provide a computer algorithm to solve an ordinary differential equation dydx=f(x,y) in the interval [a,b] for n number of discrete points, where the initial value is y(a)=α, using Euler’s method.

[2012, 12M]

3) Find dydx at x=0.1 from the following data:
x0.10.20.30.4y0.99750.99000.97760.9604

[2012, 20M]

4) Suppose a computer spends 60 per cent of its time handling a particular type of computation when running a given program and its manufacturers make a change that improves its performance on that type of computation by a factor of 10. If the program takes 100 sec to execute, what will its execution time be after the change?

[2010, 6M]

1) Using Runge-Kutta method of fourth order, solve dydx=y2−x2y2+x2 with y(0)=1 at x=0.2. Use four decimal places for calculation and step length 0.2.

[2019, 10M]

2) Solve the initial value problem dydx=x(y−x), y(2)=3 in the interval [2,2.4] using the Runge-Kutta fourth-order method with step size h=0.2.

[2015, 15M]

3) Use Runge-Kutta formula of fourth order to find the value of y at x=0.8, where dydx=√x+y, y(0.4)=0.41. Take the step length h=0.2.

[2014, 20M]

4) Find the value of y(1.2) using Runge-Kutta fourth order method with step size h=0.2 from the initial value problem: y′=xy, y(1)=2.

[2009, 15M]

5) Apply the second order Runge-Kutta method to find an approximate value of y at x=0.2 taking h=0.1, given that y satisfies the differential equation and the initial condition y′=x+y, y(0)=1.

[2007, 15M]

6) Given dydx=y−x where y(0)=2, using the Runge-Kutta fourth order method, find y(0.1) and y(0.2). Compare the approximate solution with its exact solution. (e0.1=1.10517, e0.2=1.2214)

[2002, 20M]