These functions act in the second variable as the response to a point source, leading them to be sometimes called "causal fundamental solution" or "impulse response" to an original initial-value problem, and they are deÂfined as functions that producea Dirac delta function when acted on by a linear differential operator.
Efficient numerical computation of the periodic form of these functions is possible due to Ewald's method, which was initially developed to transforms slowly convergent series representations of them for the 3D Helmholtz equation to a rapidly convergent series. To resolve a common problem that arises when the numbers of non-zero solutions for the homogeneousdirect and adjoint problems are equal, a "modifiÂed" variant of these functions can be constructed either by removing part of their boundary conditions or by subtracting from the right side of their deÂfinition a term involving the conjugate of a solution. These functions act in the second variable as the response to a point source, leading them to be sometimes called "causal fundamental solution" or "impulse response" to an original initial-value problem, and they are deÂfined as functions that producea Dirac delta function when acted on by a linear differential operator. For 10 points, identify these eponymous integral kernels used to solve differential equations.
Efficient numerical computation of the periodic form of these functions is possible due to Ewald's method, which was initially developed to transforms slowly convergent series representations of them for the 3D Helmholtz equation to a rapidly convergent series.
Green's functions