Numerical methods for differential equations – MCQs – EE

1. Which method is a simple one-step method for solving ordinary differential equations?
(A) Euler’s method
(B) Runge-Kutta method
(C) Adams-Bashforth method
(D) Finite difference method

2. Which method is more accurate than Euler’s method?
(A) Forward difference
(B) Runge-Kutta method
(C) Taylor series method
(D) Midpoint method

3. The order of accuracy of Euler’s method is:
(A) 1
(B) 2
(C) 3
(D) 4

4. Runge-Kutta fourth-order method is:
(A) One-step method
(B) Multi-step method
(C) Predictor-corrector method
(D) Implicit method

5. Multi-step methods use:
(A) Current point only
(B) Previous points and current point
(C) Exact solution
(D) Random points

6. Adams-Bashforth method is an example of:
(A) Explicit multi-step method
(B) Implicit multi-step method
(C) One-step method
(D) Predictor-corrector method

7. Adams-Moulton method is:
(A) Explicit
(B) Implicit
(C) Euler method
(D) Runge-Kutta method

8. Predictor-corrector methods combine:
(A) Explicit and implicit methods
(B) Two explicit methods
(C) Two implicit methods
(D) Euler method only

9. Stability of a numerical method is important when solving:
(A) Stiff differential equations
(B) Nonlinear equations only
(C) Algebraic equations
(D) Linear equations only

10. Stiff differential equations are characterized by:
(A) Rapid variations in some components
(B) Smooth solutions
(C) Linear behavior only
(D) Constant coefficients only

11. Implicit methods are preferred for:
(A) Stiff equations
(B) Simple linear equations
(C) Exact solutions
(D) Small datasets only

12. Euler’s method may fail for:
(A) Large step size
(B) Stiff equations
(C) Highly nonlinear systems
(D) All of the above

13. Runge-Kutta methods are:
(A) Explicit
(B) Implicit
(C) Multi-step
(D) Unstable always

14. The order of Runge-Kutta fourth-order method is:
(A) 2
(B) 3
(C) 4
(D) 5

15. In predictor-corrector methods, the predictor:
(A) Provides an initial estimate
(B) Corrects the solution
(C) Computes exact solution
(D) None of the above

16. The corrector in predictor-corrector methods:
(A) Improves the predicted solution
(B) Generates initial guess
(C) Solves algebraic equations only
(D) Reduces step size

17. Finite difference method is used to solve:
(A) Partial differential equations
(B) Ordinary differential equations only
(C) Algebraic equations
(D) Nonlinear equations only

18. Forward difference method is an example of:
(A) Explicit method
(B) Implicit method
(C) Predictor-corrector method
(D) Runge-Kutta method

19. Backward difference method is an example of:
(A) Explicit method
(B) Implicit method
(C) Euler method
(D) Runge-Kutta method

20. Crank-Nicolson method is:
(A) Explicit
(B) Implicit
(C) Predictor-corrector
(D) Euler method

21. Stability of a method improves by:
(A) Reducing step size
(B) Using implicit methods
(C) Both A and B
(D) Ignoring errors

22. Euler’s method is conditionally stable for:
(A) All step sizes
(B) Small step sizes
(C) Large step sizes
(D) Stiff equations only

23. Multi-step methods are efficient for:
(A) Large systems of differential equations
(B) Single-step problems only
(C) Algebraic equations only
(D) Linear equations only

24. Adams-Bashforth and Adams-Moulton methods require:
(A) Previous function values
(B) Only current function value
(C) Exact solution
(D) Random values

25. Runge-Kutta methods avoid:
(A) Using previous steps
(B) Reducing step size
(C) Predictor-corrector iterations
(D) Implicit computation

26. Stiffness in ODEs often occurs in:
(A) Electrical circuits with fast and slow dynamics
(B) Linear resistive circuits only
(C) Simple RC circuits
(D) Algebraic equations

27. Euler’s method error accumulates:
(A) Linearly with step size
(B) Quadratically with step size
(C) Exponentially
(D) Not at all

28. Predictor-corrector methods are:
(A) More accurate than single-step methods
(B) Less accurate than Euler’s method
(C) Same as forward difference
(D) Not used in EE

29. Implicit methods require:
(A) Solving algebraic equations at each step
(B) Only function evaluation
(C) Step size reduction
(D) None of the above

30. Runge-Kutta methods are widely used because:
(A) They are accurate and simple to implement
(B) They are implicit
(C) They require previous steps
(D) They are only for linear systems