1,721,062 research outputs found
A MATLAB code for the computational solution of a phase field model for pitting corrosion
No full textPhase field models have been widely considered to simulate corrosion dynamics characterised by moving boundaries. The benefits of using these models rely on the fact that the moving interface is implicitly treated by means of the introduction of an auxiliary variable. However, the computational cost of these methods is typically very high. In this paper we consider a model for pitting corrosion of a metallic specimen immersed in an electrolytic solution. For its numerical solution we consider a method that relies on a suitable splitting of the governing equations and on the use of exponential integrators. The use of modern MATLAB functions to evaluate the effect of matrix exponentials on a vector is crucial for the efficient implementation of the method. The software used is presented and discussed in detail, and some numerical tests are introduced to show the performance of the proposed algorithms
Numerical conservation laws of time fractional diffusion PDEs
Full text linkThis paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy discrete counterparts of these conditions have conservation laws that approximate the continuous ones. On the basis of this result, we derive conservation laws for a mixed scheme that combines a finite difference method in space with a spectral integrator in time. A range of numerical experiments shows the convergence of the proposed method and its conservation properties
Fine Tuning Numerical Schemes for PDEs
No full text“Defect” based estimates of the local truncation error are here successfully employed to obtain optimal parameters in locally conservative finite difference methods for PDEs. Numerical tests show that new proposed technique greatly improves the accuracy of the underlying methods maintaining the preservation of the conservation laws
Non-standard schemes for time-fractional reaction–advection–diffusion problems
No full textThe present paper concerns the numerical solution of time-fractional reaction–advection–diffusion problems. In real applications, an important issue is the preservation of qualitative properties of the analytical solution, such as positivity, which standard methods achieve only for small stepsizes. Here, novel explicit and implicit non-standard finite difference methods are introduced, by treating different terms in the approximations on different time levels, in a way to keep the solution non-negative at all times. A rigorous analysis of the stability and convergence of the proposed schemes is provided, offering robust theoretical results that illustrate their effectiveness in preserving positivity while generating accurate approximations of the solution. Finally, some numerical experiments demonstrate the efficacy of the proposed methods on different benchmark problems
Exponentially fitted methods with a local energy conservation law
No full textA new exponentially fitted version of the discrete variational derivative method for the efficient solution of oscillatory complex Hamiltonian partial differential equations is proposed. When applied to the nonlinear Schrodinger equation, this scheme has discrete conservation laws of charge and energy. The new method is compared with other conservative schemes from the literature on a benchmark problem whose solution is an oscillatory breather wave
A 8 years experience on the treatmentof extrahepatic biliary atresia: results in 72 cases
No full text
- …
