GENERATION OF HIGHER-ORDER FUNDAMENTAL-SOLUTIONS TO THE 2-DIMENSIONALMODIFIED HELMHOLTZ-EQUATION

The higher order fundamental solutions to the two-dimensional (2-D) mo dified Helmholtz equation have been derived. The Lth order fundamental solution has the form phi(i)(L) = A(L)(kr)L K(L)(kr), which satisfie s the equation [GRAPHICS] and the relationship of the coefficients A(L ) is given as A(L) = A(L-1)/(2Lk2) with A0 = 1/(2pi). These solutions can be used for applying the multiple reciprocity boundary element met hod to the 2-D modified Helmholtz problems. The derivation procedure s hown in the present paper can also be applied to obtaining higher orde r fundamental solutions to other engineering equations.