Central difference regularization method for inverse source problem on the Poisson equation

References

• Schuhmacher A, Hald J, Rasmussen KB, Hansen PC. Sound source reconstruction using inverse boundary element calculations. J. Acoust. Soc. Am. 2003;113:114–127.
   PubMed Web of Science ®Google Scholar
• Albanese R, Monk P. The inverse source problem for Maxwell’s equations. Inverse Prob. 2006;22:1023–1035.
   Web of Science ®Google Scholar
• Bao G, Lin J, Triki F. A multi-frequency inverse source problem. J. Differ. Equ. 2010;249:3443–3465.
   Web of Science ®Google Scholar
• He S, Romanov VG. Identification of dipole sources in a bounded domain for Maxwell’s equations. Wave Motion. 1998;28:25–40.
   Web of Science ®Google Scholar
• Atmadja J, Bagtzoglou AC. Pollution source identification in heterogeneous porous media. Water Resour. Res. 2001;37:2113–2125.
   Web of Science ®Google Scholar
• Cannon JR. One dimensional heat equation. California: Addison-Wesley Publishing Company; 1984.
   Google Scholar
• Savateev EG. On problems of determining the source function in a parabolic equation. J. Inverse Ill-Posed Prob. 1995;3:83–102.
   Google Scholar
• Yi Z, Murio DA. Source term identification in 1-D IHCP. Comput. Math. Appl. 2004;47:1921–1933.
   Web of Science ®Google Scholar
• Yan L, Yang FL, Fu CL. A meshless method for solving an inverse spacewise-dependent heat source problem. J. Comput. Phys. 2009;228:123–136.
   Web of Science ®Google Scholar
• Farcas A, Lesnic D. The boundary-element method for the determination of a heat source dependent on one variable. J. Eng. Math. 2006;54:375–388.
   Web of Science ®Google Scholar
• Ling L, Yamamoto M, Hon YC, Takeuchi T. Identification of source locations in two-dimensional heat equations. Inverse Prob. 2006;22:1289–1305.
   Web of Science ®Google Scholar
• Hon YC, Li M, Melnikov YA. Inverse source identification by Green’s function. Eng. Anal. Bound. Elem. 2010;34:352–358.
   Web of Science ®Google Scholar
• Nara T, Ando S. A projective method for an inverse source problem of the Poisson equation. Inverse Prob. 2003;19:355–369.
   Web of Science ®Google Scholar
• Farcas A, Elliott L, Ingham DB, Lesnic D, Mera NS. A dual reciprocity boundary element method for the regularized numerical solution of the inverse source problem associated to the poisson equation. Inverse Prob. Sci. Eng. 2003;11:123–139.
   Web of Science ®Google Scholar
• Jin BT, Marin L. The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction. Int. J. Numer. Methods Eng. 2007;69:1570–1589.
   Web of Science ®Google Scholar
• Yang F, Fu CL. The modified regularization method for identifying the unknown source on Poisson equation. Appl. Math. Model. 2012;36:756–763.
   Web of Science ®Google Scholar
• Yang F. The truncation method for identifying an unknown source in the Poisson equation. Appl. Math. Comput. 2011;217:9334–9339.
   Web of Science ®Google Scholar
• Kagawa Y, Sun Y, Matsumoto O. Inverse solution of poisson equation using DRM boundary element model-Identification of space charge distribution. Inverse Prob. Sci. Eng. 1995;1:247–265.
   Google Scholar
• Sun Y, Kagawa Y. Identification of electric charge distribution using dual reciprocity boundary element models. IEEE Trans. Magnet. 1997;33:1970–1973.
   Web of Science ®Google Scholar
• Eldén L. Numerical solution of the sideways heat equation by difference approximation in time. Inverse Prob. 1995;11:913–923.
   Web of Science ®Google Scholar
• Xiong XT, Fu CL, Li HF. Central difference schemes in time and error estimate on a non-standard inverse heat conduction problem. Appl. Math. Comput. 2004;157:77–91.
   Web of Science ®Google Scholar
• Xiong XT, Fu CL, Li HF. Central difference method of a non-standard inverse heat conduction problem for determining surface heat flux from interior observations. Appl. Math. Comput. 2006;173:1265–1287.
   Web of Science ®Google Scholar
• Xiong XT, Fu CL. Central difference regularization method for the Cauchy problem of the Laplace’s equation. Appl. Math. Comput. 2006;181:675–684.
   Web of Science ®Google Scholar
• Xiong XT, Fu CL, Qian Z. Two numerical methods for solving a backward heat conduction problem. Appl. Math. Comput. 2009;179:370–377.
   Web of Science ®Google Scholar
• Yang F, Guo HZ, Li XX. The method of central difference for the inverse time-dependent heat source problem. Appl. Math. Comput. 2011;218:3025–3034.
   Web of Science ®Google Scholar