Category: 06. Recurrence Relations

Generating function is a method to solve the recurrence relations. Let us consider, the sequence a0, a1, a2….ar of real numbers. For some interval of real numbers containing zero values at t is given, the function G(t) is defined by the series            G(t)= a0, a1t+a2 t2+⋯+ar tr+…………equation (i) This function G(t) is called…

The total solution or the general solution of a non-homogeneous linear difference equation with constant coefficients is the sum of the homogeneous solution and a particular solution. If no initial conditions are given, obtain n linear equations in n unknowns and solve them, if possible to get total solutions. If y(h) denotes the homogeneous solution of…

(a) Homogeneous Linear Difference Equations and Particular Solution: We can find the particular solution of the difference equation when the equation is of homogeneous linear type by putting the values of the initial conditions in the homogeneous solutions. Example1: Solve the difference equation 2ar-5ar-1+2ar-2=0 and find particular solutions such that a0=0 and a1=1. Solution: The characteristics equation…

A Recurrence Relations is called linear if its degree is one. The general form of linear recurrence relation with constant coefficient is           C0 yn+r+C1 yn+r-1+C2 yn+r-2+⋯+Cr yn=R (n) Where C0,C1,C2……Cn are constant and R (n) is same function of independent variable n. A solution of a recurrence relation in any function which satisfies the given…

A recurrence relation is a functional relation between the independent variable x, dependent variable f(x) and the differences of various order of f (x). A recurrence relation is also called a difference equation, and we will use these two terms interchangeably. Example1: The equation f (x + 3h) + 3f (x + 2h) + 6f (x…