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Exact solutions and numerical approximations of mixed problems for the wave equation with delay. (English) Zbl 1309.35045

Summary: This work deals with the construction of exact and continuous numerical solutions of mixed problems for the wave equation with delay \[ u_{tt}(t,x)=a^2u_{xx}(t,x)+bu(t-\tau,x), \quad t>\tau, \quad 0\leq x\leq l. \] 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.

MSC:

35L20 Initial-boundary value problems for second-order hyperbolic equations
35C05 Solutions to PDEs in closed form
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