### Algorithm with guaranteed accuracy for computing a solution to an initial value problem for linear difference equations

#### Abstract

Consider an initial value problem for simultaneous linear difference equations

*x(n+1) = Ax(n) + f(n), x(0) = a*, with*A*the*N**N*rational matrix, {*f(n)*} a sequence of*N*-dimensional rational vectors, and*a*a rational*N-*dimensional vector. The problem has a unique solution; but to compute {*x(n)*} in the interval [*0,M*] with*M*a nonnegative integer, we approximate the reals and carry out the elementary arithmetic operations in special way. By means of this algorithm, we solve the initial value problem for a discrete asymptotically stable matrix*A*with guaranteed accuracy.#### Keywords

initial value problems, simultaneous linear difference equations, algorithms with guaranteed accuracy, discrete asymptotically stable matrices