Error Bounds for the Truncation of Infinite Linear Differential Systems

An infinite system of linear differential equations of the form $x˙$ = Ax + f, x(0) = y is considered, where x, y and f are infinite column vectors in E, and A is a constant infinite matrix defining a bounded operator on E, where E is l₁, (c₀), or l_∞. Explicit error bounds are obtained for the approximation of the solution of the infinite system by the solutions of the finite truncated systems.