[PDF] Top 20 Algorithm Analysis of Numerical Solutions to the Heat Equation

... Heat equation has many applications in engines and structural ...diffusion equation and models the diffusion of substances such as drugs, bacterial, or viral spread in the human ...appropriate ... See full document

... of numerical methods have been proposed for fractional differential equations [5, 6, 7, 8, 9, 10, ...telegraph equation, which have parabolic ...telegraph equation than by the heat ... See full document

... accurate numerical simulations for many practice problem ...parallel numerical solutions for PDEs have two ...for heat equation in one-dimensional geometry with large step length ... See full document

... the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, ...Burgers’ equation into the linear heat ...merical ... See full document

... R., ''Some Numerical Results for the Solution of the Heat Equation Backwards in Time," Numerical Solutions of Nonlinear Differential Equations.. and Hilbert D., Methods of Mathematical P[r] ... See full document

... find solutions that are invariant with respect to trans- formation groups, we must investigate a second-order linear equation with re- spect to V ( ) ξ , which depends on σ ...by numerical studies, ... See full document

... the solutions of the Alfven wave kinetic equation, there is growing evidence [25, 38, 44] that finite capacity cascade often, if not always, exhibit a dynamical scaling anomaly during the transient stage of ... See full document

... Dirac equation was analyzed with an arbitrary electric potential depending upon one spacial ...Dirac equation into a pair of partial differential ...Vekua equation, as stated in [11], that is indeed ... See full document

... Schrödinger equation, in which the normal Schrödinger equation is generalized in anal- ogy with fractional ...this equation in the case of the one-dimensional infinite square well ...troduced ... See full document

... simple equation; see ...modern numerical integration; and it was an important precursor to the development of the calculus by Isaac Newton and Gottfried ...developing numerical procedures was the ... See full document

... Allen-Cahn equation satisfies the maximum principle and energy ...for numerical approximation solutions? In 2010, Shen Jie established first-order semi-implicit scheme, second-order semi-implicit ... See full document

... of solutions on multiple meshes, fulfillment of the energy balance conditions at boundaries of the calculation ...the numerical analysis did not exceed ... See full document

... Babayar-Raz an inhomog integration Mathematics Babayar-Raz integration m conduction Mathematics Orsi A. P. equations of kernels. Math Criscuolo G Convergence weakly sing 55(191): 213 Babayar-Raz solution for s ... See full document

... the numerical solution of the MEW equation using quintic B-spline collocation ...MEW equation by collocation method using quintic B-spline finite elements and obtained the numerical solution ... See full document

... me [25]. The accuracy of erical computations s checked by testing different time and space steps. The variables t and x are measured in units of time and space, respectively. In this study, we consider the input tem- ... See full document

... the numerical so- lution of FPDEs have been ...reliable numerical scheme is a problem of fundamental ...of numerical methods have been proposed for obtaining approximate solutions to FPDEs [1, ... See full document

... homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic ...The numerical results obtained are compared with the results obtained by using variational iteration ... See full document

... a heat pipe reached a fully steady-state condition, where the vapor flow is in the continuum state, it is often desirable to determine the length of time needed to reach another steady state for a given increase ... See full document

... approximating solutions of partial differential equa- tions (PDE) ( Awanou et ...approximating solutions of spherical PDE in spherical spline spaces as well (Baramidze and Lai ...a numerical ... See full document

... the heat equation and appropriate boundary conditions and their numerical simulations with the Finite Element ...internal heat generation, thermal conductivity and other physical and ... See full document