Exact solutions and numerical approximations of mixed problems for the wave equation with delay

This work deals with the construction of exact and continuous numerical solutions of mixed problems for the wave equation with delayutt(t,x)=a2uxx(t,x)+bu(t-τ,x),t>τ,0⩽x⩽l.Using the method of separation of variables, and obtaining explicit expressions for the solution of a general initial value problem for a second order delay differential equation, an exact infinite series solution is derived. Bounds on the truncation errors, when this series is approximated by finite sums, are given, thus providing constructive continuous numerical solutions with prescribed accuracy in bounded domains.