Related papers: A Chebyshev multidomain adaptive mesh method for R…
We present two new quantum algorithms for reaction-diffusion equations that employ the truncated Chebyshev polynomial approximation. This method is employed to numerically solve the ordinary differential equation emerging from the…
This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of high-power laser diodes, either broad area lasers, index guided lasers or monolithic master oscillator power amplifier devices.…
In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite $k$-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
We consider reaction-diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using Lyapunov functional and duality arguments, we establish…
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time,…
A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem is unstable and approximation properties do not hold. The…
This paper proposes a new numerical method based on the Chebyshev wavelets (CWs) to solve the variable-order time fractional mobile-immobile advection-dispersion equation. To do this, a new operational matrix of variable-order fractional…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…
We present a novel continuous time trajectory representation based on a Chebyshev polynomial basis, which when governed by known dynamics models, allows for full trajectory and robot dynamics estimation, particularly useful for…
In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two-dimensional multi-order time-fractional partial differential equations; nonlinear and linear in respect to spatial and temporal…
The motivation of this work is to produce an integrated formulation for material response due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of…
The stepwise coupled-mode model is a classic approach for solving range-dependent sound propagation problems. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…