Numerical Methods Quiz

Which of the following is an iterative method for finding the root of a nonlinear equation?

• Gaussian Elimination

• Newton-Raphson Method

• Trapezoidal Rule

• Simpson’s Rule

In numerical methods, what is the primary cause of truncation error?

• Errors due to rounding during computations

• Errors from stopping an infinite process (e.g., Taylor series) after a finite number of terms

• Errors caused by insufficient computer memory

• Errors from incorrect input data

The Trapezoidal Rule for numerical integration works by approximating the area under the curve as:

• A series of rectangles

• A series of parabolas

• A series of triangles

• A series of trapezoids

Which of the following methods is not commonly used to solve a system of linear equations?

• Gaussian Elimination

• Newton-Raphson Method

• A series of triangles

• A series of trapezoids

A numerical method is said to be stable if:

• It produces exact results for all problems

• Errors do not grow significantly as computations progress

• It can only handle small datasets

• It converges to zero for any initial condition

Which of the following statements is true about the Bisection Method?

• It requires the derivative of the function.

• It guarantees convergence if the function changes sign over the interval.

• It is faster than the Newton-Raphson Method.

• It works only for quadratic equations.

Simpson’s Rule provides an approximation for integrals by assuming the function can be approximated by:

• A straight line

• A cubic polynomial

• A parabola

• A series of trapezoids

In the context of iterative methods, what does convergence mean?

• The method stops after a fixed number of steps.

• The method produces exactly the true solution.

• The approximate solution approaches the true solution as iterations increase.

• The method works for all equations.

Which step in Gaussian Elimination involves making the matrix upper triangular?

• Backward substitution

• Forward elimination

• Iteration

• Pivoting

The fourth-order Runge-Kutta method achieves higher accuracy by:

• Using a larger step size h.

• Using weighted averages of slopes at intermediate points.

• Solving the ODE analytically.

• Using backward difference approximations.