Numerical Methods Viva

Numerical methods viva – viva – voce questions Experiment no. 1: C program for finding smallest positive root of an equation by Bisection method

1) What do you mean by root of an equation? 2) In bisection method every time we reduce the interval by half? 3) What is intermediate value theorem? 4) Does bisection method give guarantee of convergence? 5) As compared to other iteration methods, does bisection method takes more number of iterations? 6) Do we apply intermediate value theorem repeatedly in bisection method? 7) What is the graphical meaning of Bisection method? 8) Explain bisection method? 9) What is the use of f unction fabs in C? 10) What is the use of f unction sqrt in C? 11) Name some commonly used mathematical functions in C? 12) Name some commonly used header files in C? 13) What is the syntax of for loop in C? 14) What is the syntax of if loop in C? 15) What are the different methods of finding root of an equation? 16) What is the difference between library functions and user defined functions i n C? 17) What is the formula for finding the root by using the bisection method? 18) What is the formula of iteration by bisection method? 19) What are the variables a and b in bisection method program? 20) What is aerr in bisection method program? 21) What is maxitr in bisection method program?

Experiment no. 2: C program for finding smallest positive root of an equation by Newton-Raphson method 1) Does Newton-Raphson method give guarantee of convergence? 2) What is the use of function fabs in C? 3) As compared to other iteration methods, does Newton-Raphson method takes less number of  iterations? 4) What is the graphical meaning of Newton-Raphson method? 5) The process of finding the roots of equation is called? 6) Which are the different equations whose solution/roots we can directly find out? 7) What is iterative method of finding the root of an equation? 8) What do you mean by bracketing method? 9) Which are the different bracketing methods? 10) The root lies in between which two points? 11) Explain Newton-Raphson method? 12) Whether the Newton-Raphson method is bracketing method or open end method? 13) What do you mean by transcendental equations? 14) What is the difference between linear and non linear equation? 15) What is the formula of iteration by newton-raphson method? 16) What do mean by call by value with reference to functions? 17) What do you mean by iteration? 18) A program in C always starts with ___________function? 19) What are the different types of variables in C? 20) What do you mean by syntax error in C? 21) What do you mean by logical error in C? 22) What is the graphical meaning of successive approximation method? 23) What is aerr in Newton-Raphson method program? 24) What is maxitr in Newton-Raphson method program?

Experiment no. 3: C program for finding smallest positive root of an equation by false position method 1) Does false position method guarantee of convergence? 2) What is the use of function fabs in C? 3) What is the difference between false position method and secant method? 4) Which are the equations whose roots we cannot directly find out? 5) Whether the false position method is bracketing method or open end method? 6) The false position method is also called as? 7) The degree of every algebraic equation which denotes? 8) What is the formula for finding the root of the equation by using the false positi on method? 9) Explain false position method? 10) What is the formula of iteration by secant method? 11) What is the formula of iteration by false-position method? 12) What is the formula of iteration by successive approximation method? 13) What is stopping criteria for finding root of an algebraic equation? 14) In successive approximation method which condition should be satisfied by Ф( x ) to be valid? 15) Successive approximation method is also known as? 16) What is aerr in false position method program? 17) What is maxitr in false position method program?

Experiment no. 4: C program for Simultaneous linear algebraic equations by Gauss Elimination method 1) What do you mean by augmented matrix? 2) Apart from gauss elimination methods what are other methods to find solution of simultaneous linear equations? 3) How we find out co-factor of an element? 4) What do you mean by upper triangular matrix? 5) What do you mean by square matrix? 6) What is the syntax of for loop in C? 7) What are the advantages of studying numerical methods? 8) What is floating point representation of numbers? 9) What is normalization of numbers? 10) What do you mean by significant digits? 11) What do you mean by back substitution in gauss elimination method? 12) What is the difference between Gauss-Jacobi and gauss-Siedel method? 13) Of the two methods Jacobi and Gauss-Siedel which one requires more iteration to converge? 14) What is matrix inversion method for solving simultaneous algebraic equations? 15) What is characteristic equation? 16) Can an Eigen value have multiple Eigen vectors? 17) What do you mean by normalized Eigen vector? 18) Is Gauss-Siedel a direct type method? 19) Is Gauss-Jacobi an iterative method? 20) Matrix inversion method is direct method? True or false? 21) Gauss-elimination method is an iterative method? True or false?

Experiment no. 5: C program for finding value of y corresponding to value of x by Newton’s Forward Interpolation method 1) What is the syntax of for loop in C? 2) Which Newton’s interpolation formula is used to find out value of function near the beginning or before the tabulated values? 3) Which Newton’s interpolation formula is used to find out value of function near the end or ahead of  the tabulated values? 4) Can Newton’s forward interpolation formula be used for data points with unequal intervals? 5) Can Newton’s backward interpolation formula be used for data points with unequal intervals? 6)

Name some techniques other than Newton’s forward interpolation for interpolating a polynomial?

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What is the difference between forward differences and backward differences?

8) Is the value of forward and backward differences unequal? 9) What do mean by step size h? 10) What is p in Newton Forward interpolation formula? 11) What is Δy 0 in Newton Forward interpolation formula? 2 12) What is Δ y 0 in Newton Forward interpolation formula?

13) What is p in Newton Backward interpolation formula? 14) What is y n in Newton Backward interpolation formula? 2

15) What is  y n in Newton Backward interpolation formula? 16) What do you mean by slope at any point on the curve? 17) What do you mean by interpolating polynomial? 18) What is Taylor series? 19) What do you mean by first order difference in interpolation with equal intervals? 20) What do mean by second order difference in interpolation with equal intervals? 21) If the number of data pairs in case of interpolation is n then which order differences are going to be zero? 22) Why we have used 2-D array for saving differences in Newton forward interpolation?

Experiment no. 6: C program for finding value of y corresponding to value of x by Lagrange’s Interpolation method 1) What do you mean by unequal intervals? 2) What do mean by entry? 3) What do you mean by arguments? 4) Which technique other than Lagrange’s interpolation is used for interpolation of data points with unequal intervals? 5) What is the syntax of for loop in C? 6) What is inverse lagrange’s interpolation? 7) Objects are ___________of classes? 8) Classes are ____________for objects? 9) What is procedure oriented programming? 10) What are drawbacks of procedure oriented programming? 11) Does data flow freely in object oriented program? 12) What do you mean by reusability with reference to OOP? 13) What do you mean by extensibility with reference to OOP? 14) Name few main characteristic of procedure oriented programming? 15) What is Lagrange’s inverse interpolation formula? 16) What is 2-D array in C programming? 17) What is the difference between Lagrange’s interpolation and Lagrange’s inverse interpolation? 18) Does interpolating polynomial exactly fits the given data? 19) What is the difference between interpolation and approximations? 20) What do you mean by divided difference in interpolation with unequal intervals?

Experiment no. 7: C program for finding value of integral of a function by trapezoidal rule 1) What is the syntax of for loop in C? 2) From which basic formula we derive trapezoidal rule? 3) The format specifier for integer type variable is? 4) The format specifier for float type variable is? 5) What are different operators used in C? 6) What do you mean by precision? 7) Can a decimal number be exactly represented in binary form? 8) What do you mean by data errors? 9) What do you mean by conversion errors? 10) What do you mean by numerical errors? 11) What do you mean by round off errors? 12) What do you mean by truncation errors? 13) What is n in numerical integration? 14) What is formula of trapezoidal rule for f inding integral of a given function? 15) What do you mean by data encapsulation? 16) What do you mean by data abstraction? 17) What is base class? 18) What is derived class? 19) What is the formula for k 1 in RK-4 method? 20) What is the formula for k 2 in RK-4 method?

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Experiment no. 8: C program for finding value of integral of a function by Simpson’s 1/3

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1) What is y0 in Simpson’s formula? 2) What is yn in Simpson’s formula? 3) What is h in Simpson’s formula? rd

4) What are the methods other Simpson’s 1/3 rule for numerical integration? rd

5) In Simpson’s 1/3 rule the number of intervals should always be an __________ number? rd

6) Simpson’s 1/3 rule gives better result than trapezoidal rule? T rue or false? rd

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7) Simpson’s 1/3 rule gives better result than Simpson’s 3/8 rule? 8) Which method can be further applied to improve the accuracy of Simpson’s 1/3 rd rule? 9) What is the syntax of for loop in C? 10) What is formula of Simpson’s 1/3rd rule for finding integral of a given function? 11) What is n in numerical integration? 12) What is the formula for k 3 in RK-4 method? 13) What is the formula for k4 in RK-4 method? 14) What is the use of clrscr() function? 15) What is the use of getch() function?

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Experiment no. 9: C program for finding value of integral of a function by Simpson’s 3/8 rule 1) What is the syntax of for loop in C? 2) What are different types of errors? 3) What do you mean by inherent errors? 4) What do you mean by accuracy? 5) What is formula of Simpson’s 3/8th rule for finding integral of a given function? 6) What is n in numerical integration? rd

7) In Simpson’s 1/3 rule the number of intervals should always be an __________ number? rd 8) Simpson’s 1/3 rule gives better result than trapezoidal rule? True or false? rd th 9) Simpson’s 1/3 rule gives better result than Simpson’s 3/8 rule? 10) What is Taylor series method to solve ordinary differential equation? th

11) What is y0 in Simpson’s 3/8 formula? th

12) What is yn in Simpson’s 3/8 formula? 13) What is the graphical meaning of Euler’s method? 14) What is the graphical meaning of modified Euler’s method? 15) What is the formula for Δ y in Runge-Kutta fourth order method? 16) Runge-Kutta second order method is nothing but _______________modified Euler’s method? 17) What do you mean by dynamic binding in OOP? 18) What is the syntax of while loop in C? 19) What is the syntax of do-while loop in C? 20) What is the use of return function? 21) Every statement in C language should end with a ____________?

Experiment no. 10: C program for finding value of integral of a function having limit from -1 to 1 by 2 point and 3 point Gauss quadrature formula 1) What are two types of gauss quadrature formula? 2) What does the function sqrt do? 3) What is the syntax of for loop in C? 4) What is the of 3-point gauss quadrature formula for finding integral of a given function whose limits is from -1 to 1? 5) What is the of 2-point gauss quadrature formula for finding integral of a given function whose limits is from -1 to 1? 6) In solving problem for integration by gauss quadrature formula, if the limit is not from -1 to 1 then how we convert the limits? 7) What is the difference between 2 point and 3 point gauss quadrature formula? 8) How we solve simultaneous differential equation by RK-4 method? 9) How we solve second order differential equation by RK-4 method? 10) In finite difference method we replace y” by what equation? 11) In finite difference method we replace y’ by what equation? 12) What do you mean by objects in OOP? 13) What do you mean by classes in OOP? 14) What is inheritance in OOP? 15) What is polymorphism in OOP? 16) What do you mean by message passing in OOP? 17) Name few applications of OOP? 18) Classes are user-defined data types? True or false? 19) What is the variable s in program? 20) What is the variable s1 in program? 21) What is the variable s2 in program?