Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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01 Jan 1939
TL;DR: On operations Functions important in the calculus of finite differences Inverse operation of differences and means, expansion of functions, interpolation, construction of tables Approximation and graduation Numerical solution of equations.
Abstract: On operations Functions important in the calculus of finite differences Inverse operation of differences and means. Sums Stirling's numbers Bernoulli polynomials and numbers Euler's and Boole's polynomials. Sums of reciprocal powers Expansion of functions, interpolation, construction of tables Approximation and graduation Numerical solution of equations. Numerical integration Functions of several independent variables Difference equations Partial difference equations.
528 citations
TL;DR: In this paper, the authors investigated the accuracy and stability of an implicit numerical scheme for solving the fractional diffusion equation and provided algebraic and numerical evidence that the scheme is unconditionally stable for 0<@c=<1.
525 citations
TL;DR: In this paper, the authors present a review of the main components of calculation methods, based on the solution of conservation equations in differential form, for the velocity, temperature and concentration fields in turbulent combusting flows.
522 citations
TL;DR: In this article, a semi-implicit discretization for the convective Cahn-Hilliard equation with high-resolution schemes employed for direct numerical simulations of turbulence is proposed.
512 citations
TL;DR: In this article, a finite-difference beam propagation method (FD-BPM) is outlined and assessed in comparison with conventional beam propagation methods which use fast Fourier transformation.
Abstract: A finite-difference beam propagation method (FD-BPM) is outlined and assessed in comparison with a conventional beam propagation method (FFT-BPM) which uses fast Fourier transformation. In the comparative study three straight waveguides with different index profiles that are frequently encountered in integrated optics are utilized. Using both methods normalized effective index values of the eigenmodes of these waveguides are calculated and compared with the exact values obtained from analytical expressions. As a further accuracy criterion, the power loss due to numerical errors when an eigenmode of a waveguide is excited is evaluated. Based on this comparison the accuracy, computational efficiency, and stability of the FD-BPM are assessed. >
508 citations