The annihilator method for computing particular solutions to partial differential equations

• Published in: Engineering analysis with boundary elements Vol. 23; no. 3; pp. 275 - 279
• Main Authors: Golberg, M.A., Chen, C.S., Rashed, Y.F.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.1999; Elsevier
• Subjects: Annihilator method; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Helmholtz equation; Mathematical methods in physics; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Particular solution; Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Thin plate spline; Helmholtz equation; Annihilator method; Particular solution; Thin plate spline; Annihilation; Boundary value problem; Differential equation; Thin plate; Numerical method; Non linear effect; Structural analysis; Spline approximation
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/S0955-7997(98)00081-2

We generalize the well-known annihilator method, used to find particular solutions for ordinary differential equations, to partial differential equations. This method is then used to find particular solutions of Helmholtz-type equations when the right hand side is a linear combination of thin plate and higher order splines. These particular solutions are useful in numerical algorithms for solving boundary value problems for a variety of elliptic and parabolic partial differential equations.