EVEREST ENGINEERING AND MANAGEMENT COLLEGE
BE (Electronic and Computer)
Tutorial -5 & 6
1. Solve the differential equation by using 4th order R-K method for
y (0.6) from
dy
 x 2  y 2 y (0)  3 taking h = 0.3
dx
2. Use RK2 method to solve y" = xy' – y; y(0) = 3, y’(0) = 0 to approximate y (0.2), take
h = 0.1
3. A steel plate is of size 15 cm × 15 cm. If two of the sides are held at 100 0C and other
two sides are held at 0 0C, what is the steady state temperature at interior points
assuming a grid size of 5 cm × 5 cm?
4. Solve the differential equation for y (0.25) using RK 4th order method.
2
d 2 y  dy 
10 2     6 x  0 , with y(0) = l and y1(0) = 0. (take h = 0.25).
dx
 dx 
5. Solve the differential equation y1 = x + y using appropriate method within 0  x  0.2
with y(0) = 1.
6. Solve the Poisson equation,  2 f= 2x2y2 over the square domain 0 ≤x ≤3 and 0≤ y ≤3
with f= 0 on the boundary with h=1. Show the necessary steps for solving simultaneous
equations by any of the method known to you.
7. Use the classical R.K. method to estimate y(0.4) when y|(x) = x2+y2 with y(0)= 0.
Assume h = 0.2.
8. Solve the poisson equation 2f= 2x2y2 over the square domain 0x3 and 0y3 with f= 0 on
the boundary and h = 1
9. Solve the second order differential equation
y”-x2y’-2xy = 0 for y(0.1) and y’(0.1), given that
y(0)=1, y’(0)=0 using Heun’s method. Take step size h=0.1.
10. For the equation dy/dx=x-y.y(0) =1.Find the value of y when x = 0.1, 0.2, Taking h =0.1 using RK4
method.
11. Solve the Poisson equation,  2 f = 2x2y2 over the square domain 0 < x < 3 and 0 < y < 3 with f =
0 on the boundary with h = 1. Show the necessary steps for solving the simultaneous equations
by any of the method known to you
12. Find the value of x at 2.0, using Heun's Method.
y'  x  y 2 ; y(1)  8, step size h  0.5.
13. Solve: y' '2 y'6 y  x using RK  4 th Method .Where y(0)  0, y' (0)  1 are
the
initial
condition and find it for y(0.2) taking h = 0.2
14. A square metal sheet of side 30cm is floating in water such a way that two sides are in held 90 0 and
another two sides are in 100 celcius. Calculate the interior temperature of the grid of size 10cm. solve the
necessary equation using Gauss Seidal method.
15. Solve the Poisson equation ▼2f=2x2+ y, over the square domain
1≤x ≤4, 1≤y ≤4, with f=0 on the boundary. Take h=k=1
16. Solve the second order differential equation
y' ' x 2 y'2 xy  0 for y(0.1) and y'(0.1), given that y(0) = 1, y'(0)=0 using Heun's method Take
step size h = 0.1
17. Use the Rk4 method to estimate y(0.5) of the following equations with h = 0.25
dy
 x  y, y (0)  1
dx
18. Solve the differential equation
dy
= x3 + y2, y (0) = 0 for y (0.5) by Euler’s method.
dx
19. Use the classical 4th order RK method to estimate y (0.5) of the differential equation with h =
0.25,
dy
 y  sin x ; y (0)  2
dx
20. Solve the equation  2 u   10 ( x 2  y 2  10) over the square mesh with sides x = 0, y = 0, x =
3, y = 3 with u = 0 on the boundary and mesh length h = 1.
21. In a square bar with dimension of 3 inch  3 inch, torsion function,  , can be obtained from the
 2  2

  2 where  = 0 on the outer boundary of the bar's crossfollowing P.D.E:
x 2 y 2
section. Subdivide the region into nine equal squares to form a mesh and find the values of  in
the interior nodes.
22. Solve the Poisson's equation  2 u  2 x 2 y 2 over the square domain 0 <x <3 and 0 < y <3 with
Dirichlet boundary condition of u(x, y) = 0 and h = k = 1 using Gauss-Seidel method.
23. Use the classical Runge-Kutta method to estimate y(0.4) of the following equation with h = 0.2.
y | ( x)  x 2  y 2 , y(0)  0
24. Solve the Laplace’s equation Uxx + Uyy = 0 in the domain of the figure given below:
25. Solve the Poission equation  2 f  (1  x 2 ) y , over the square domain of 0  x  3 and
0  y  3 with f  0 and h  1 .
26. Solve the following differential equation within 0  x  0.5 using RK 4th order method.
2
d 2 y  dy 
10 2     6 x  0 , with y (0)  1 and y ' (0)  0 . (take h=0.25)
dx
 dx 
27. Using shooting method solve the equation
d2y
 6 x, y (1)  2, y (2)  9 in the interval (1, 2).
dx 2
28. Solve the Laplaces equation Uxx+Uyy = 0 in the domain of figure given below by Gauss Seidel
method. Obtain the solution correct to two decimal places.
29. Solve the following first order differential equation using Runge-Kutta fourth order (RK-4)
knowing an initial condition y(0) =1. Take step length of h = 0.2 and evaluate the ordinate y at x
= 1. For the same step length h, solve once again using Euler’s method and verify with the
results obtained.
dy
 x  y2
dx
30. Solve the Poission equation  2 f  (1  x 2 ) y , over the square domain of 0  x  3 and
0  y  3 with f  0 and h  1 . BY :Saroj Dhakal “EEMC “