  We propose in this paper a new numerical method to solve an inverse source
problem for general hyperbolic equations. This is the problem of reconstructing
sources from the lateral Cauchy data of the wave field on the boundary of a
domain. In order to achieve the goal, we derive an equation involving a
Volterra integral, whose solution directly provides the desired solution of the
inverse source problem. Due to the presence of such a Volterra integral, this
equation is not in a standard form of partial differential equations. We employ
the quasi-reversibility method to find its regularized solution. Using Carleman
estimates, we show that the obtained regularized solution converges to the
exact solution with the Lipschitz-like convergence rate as the measurement
noise tends to 0. This is one of the novelties of this paper since currently,
convergence results for the quasi-reversibility method are only valid for
purely differential equations. Numerical tests demonstrate a good
reconstruction accuracy.
