Question

2. True (T) or False (F) a) Round-off errors increase with the number of calculations performed b) Newton-Raphson method always converge c) Romberg formula is one of the most popular method for numerical integration d) The error of fourth order Runge-Kutta method is greater than the error of Heun method e) First order Runge-Kutta method is equivalent to the Euler method 1) A system of 2 ordinary differential equations requires 2 initial conditions to be solved g) Gauss quadrature formula cannot be used for data tables h) System of nonlinear equations can be solved using Gaussian elimination i) Solution of system of nonlinear equations requires to find partial derivatives j) Characteristic polynomial method requires to find a determinant

Answer 1

a. False. Round error decreases with no of calculations

b.False. It may converge of diverge dependig on the initial value taken.

c. True

d.True. Heun method ireferred as Improved method of Euler method for this reason

E. True

f. True. the solution will have two unknowns and two equations.

g.True

h.True

i.True

j.True