Inverse method has wide application on medical diagnosis where non-destructive evaluation is the key factor .Back scattered waves or echoes generated from the forward moving waves has information about its geometry, size and location. In this paper we have investigated how well different geometries of the object is determined from the back scattered waves by a high accuracy Non-Standard Finite Difference Time Inverse (NSFD-TI) Maxwell’s algorithm and how the refractive index of the object plays a deterministic role on its size.

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1. L. W. Schmerr, Jr., in Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach, (Plenum Press, New York, 1998).
2. R. Mickens, E, in Nonstandard finite difference models of differential equations, (World Scientific Publishing Co., Inc., River Edge, NJ, 1994).
3. K. S. Kunz, and R. J. Luebbers, in The Finite Difference Time Domain Method for Electromagnetics, (CRC Press, New York, 1993).
4. J. B. Cole, S. Banerjee, and M. Haftel, in Advances in the Applications of Nonstandard Finite Difference Schemes, ed. R. E. Mickens (World Scientific Singapore, 2007), Chap.4.
5. R. Sorrentino, L. Roselli, and P. Mezzanotte, “Time reversal in finite difference time domain method,” IEEE Microw. Guid. Wave Lett. 3(11), 402–404 (1993). [CrossRef]
6. P. W. Barber, and S. C. Hill, in Light Scattering by Particles: Computational Methods, (World Scientific, Singapore, 1990).
7. J. B. Cole, “High-Accuracy Yee algorithm Based on Nonstandard Finite Difference: New Developments and Verifications,” IEEE Trans. Antenn. Propag. 50(9), 1185–1191 (2002). [CrossRef]
8. H. Kudo, et al., “Numerical Dispersion and Stability Condition of the Nonstandard FDTD Method” Electronics and Communications in Japan, 85, 22–30(2002), http://www3.interscience.wiley.com/cgi-bin/fulltext/93514073/PDFSTART .

IEEE Microw. Guid. Wave Lett.

• R. Sorrentino, L. Roselli, and P. Mezzanotte, “Time reversal in finite difference time domain method,” IEEE Microw. Guid. Wave Lett. 3(11), 402–404 (1993). [CrossRef]

IEEE Trans. Antenn. Propag.

• J. B. Cole, “High-Accuracy Yee algorithm Based on Nonstandard Finite Difference: New Developments and Verifications,” IEEE Trans. Antenn. Propag. 50(9), 1185–1191 (2002). [CrossRef]

Other

• H. Kudo, et al., “Numerical Dispersion and Stability Condition of the Nonstandard FDTD Method” Electronics and Communications in Japan, 85, 22–30(2002), http://www3.interscience.wiley.com/cgi-bin/fulltext/93514073/PDFSTART .
• P. W. Barber, and S. C. Hill, in Light Scattering by Particles: Computational Methods, (World Scientific, Singapore, 1990).
• L. W. Schmerr, Jr., in Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach, (Plenum Press, New York, 1998).
• R. Mickens, E, in Nonstandard finite difference models of differential equations, (World Scientific Publishing Co., Inc., River Edge, NJ, 1994).
• K. S. Kunz, and R. J. Luebbers, in The Finite Difference Time Domain Method for Electromagnetics, (CRC Press, New York, 1993).
• J. B. Cole, S. Banerjee, and M. Haftel, in Advances in the Applications of Nonstandard Finite Difference Schemes, ed. R. E. Mickens (World Scientific Singapore, 2007), Chap.4.

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