Advanced scientific computer equations

H.G. Bock, Recent advances in parameter identification for ordinary differential equations, in Progress in Scientific Computing, vol. 2, (Eds. ... 

Originally proposed by K. S. Yee in 1966 [1], the FDTD technique has emerged as a foremost numerical tool for the solution of the time-dependent Maxwell s equations in either differential or integral form. As computing facilities became faster and more widely accessible, its premises found tremendous applications and proved their superiority in radiation and scattering problems. Motivated by these advances, the scientific community introduced numerous enhancements to the initial idea that greatly broadened its applicability. 

During the last 40 years, computer-based computational methods, such as molecular dynamics and Monte Carlo simulations, have evolved from advanced techniques accessible only to a few speciahsts, to standard calculation approaches available to both scientists and engineers. Similarly, numerical methods of solving the Schrodinger equation, implemented in computational softwares such as Gaussian or Materials studio, are now commonly used to study complex systems. Proper modehng of those systems plays more and more important role in modem scientific research. 

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