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On the Stability of IMEX Upwind gSBP Schemes for 1D Linear Advection-Diffusion Equations
A fully discrete energy stability analysis is carried out for linear advection-diffusion problems discretized by generalized upwind...
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Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative
In this paper, we provide an accurate numerical solution for space-time fractional linear diffusion equation involving the fractinal Caputo-Hadamard...
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Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations
The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a...
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Reduced Basis Approach for Convection-Diffusion Equations with Non-linear Boundary Reaction Conditions
This paper aims at an efficient strategy to solve drift-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous...
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Sequential Improvement Method in Probabilistic Criteria Optimization Problems for Linear-in-State Jump Diffusion Systems
AbstractHere we study the problems of probabilistic and quantile optimization of multidimensional controllable jump diffusion. As the main tool we...
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An efficient preconditioner for linear systems arising from high-order accurate schemes of time fractional diffusion equations
In this paper, we study preconditioners for all-at-once systems arising from the discretization of time-fractional sub-diffusion equations. Due to...
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Hybridizable discontinuous Galerkin method with mixed-order spaces for non-linear diffusion equations with internal jumps
We formulate a hybridizable discontinuous Galerkin method for parabolic equations with non-linear tensor-valued coefficients and jump conditions...
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Reaction-Diffusion Problems
In this chapter, we start by investigating the adsorption-desorptionAdsorption-desorption (process, phenomenon, boundary conditions, etc.) Boundary...
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Long-time behaviour of hybrid finite volume schemes for advection–diffusion equations: linear and nonlinear approaches
We are interested in the long-time behaviour of approximate solutions to anisotropic and heterogeneous linear advection–diffusion equations in the...
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The Diffusion Equation
The diffusion equation appears in many applications in science and engineering, and computational physiology is no exception. In its most basic form,...
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Inhomogenous Marketing Mix Diffusion
In this article we extend the Marketing Mix Diffusion (MMD) model to inhomogenous networks (i.e. complex networks of arbitrary topology). The...
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SUSHI for a Non-linear Time Fractional Diffusion Equation with a Time Independent Delay
We establish a linear implicit finite volume scheme for a non-linear time fractional diffusion equation with a time independent delay in any space...
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EDP-convergence for a linear reaction-diffusion system with fast reversible reaction
We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We...
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Mesh Conditions of the Preserving-Maximum-Principle Linear Finite Volume Element Method for Anisotropic Diffusion-Convection-Reaction Equations
We develop mesh conditions for linear finite volume element approximations of anisotropic diffusionconvectionreaction problems to satisfy the...
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Dual Variational Approach to Nonlinear Diffusion Equations
This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers...
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A new and efficient approach for solving linear and nonlinear time-fractional diffusion equations of distributed order
This paper is concerned with a computational approach based on the Jacobi wavelets for linear and nonlinear time-fractional diffusion equations of...
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L1 Method on Nonuniform Meshes for Linear Time-Fractional Diffusion Equations with Constant Time Delay
This paper is concerned with numerical solution of the linear time-fractional diffusion equations with constant time delay. First we investigate the...
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Unconditionally Positive, Explicit, Fourth Order Method for the Diffusion- and Nagumo-Type Diffusion–Reaction Equations
We present a family of novel explicit numerical methods for the diffusion or heat equation with Fisher, Huxley and Nagumo-type reaction terms. After...
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Fractional Anomalous Diffusion
In this chapter, we discuss the general problem of fractional diffusion equationFractional diffusion equation in connection with the anomalous...
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Degenerierte Diffusion
WirPoröse-Medien-Gleichung setzen hier unsere Untersuchungen zur Evolutionsgleichung (19.1) fort. Im vorangegangenen Kapitel haben wir ausgenutzt,...