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, withA theNN rational matrix, {f(n)} a sequence ofN-dimensional rational vectors, anda a rationalN-dimensional vector. The problem has a unique solution; but to compute {x(n)} in the interval [0,M] withM 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 matrixA with guaranteed accuracy.

Keywords


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

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