arXiv subjects

Jungang Wang

Publications and source records attributed to Jungang Wang.

6 recordsLinked to original sources

arXiv2021

An advanced meshless approach for the high-dimensional multi-term time-space-fractional PDEs on convex domains

In this article, an advanced differential quadrature (DQ) approach is proposed for the high-dimensional multi-term time-space-fractional partial differential equations (TSFPDEs) on convex domains. Firstly, a family of high-order difference schemes is introduced to discretize the time-fractional derivative and a semi-discrete scheme for the considered problems is presented. We strictly prove its unconditional stability and error estimate. Further, we derive a class of DQ formulas to evaluate the fractional derivatives, which employs radial basis functions (RBFs) as test functions. Using these DQ formulas in spatial discretization, a fully discrete DQ scheme is then proposed. Our approach provides a flexible and high accurate alternative to solve the high-dimensional multi-term TSFPDEs on convex domains and its actual performance is illustrated by contrast to the other methods available in the open literature. The numerical results confirm the theoretical analysis and the capability of our proposed method finally.

math.NA↗

arXiv2019

Finite Element Methods for Fractional PDEs in Three Dimensions

This paper is a generalization of the previous work (Yang et.al, J. Comput. Phys. 330 (2017), 863-883) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions are given and a path searching method is developed to find the integration paths corresponding to the Gaussian points. Moreover, a template matrix is introduced to speed up the procedures. Numerical experiments on a steady problem are presented verifying the efficiency of proposed techniques.

math.NA↗

arXiv2018

Effective numerical treatment of sub-diffusion equation with non-smooth solution

In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a smooth operator, we devise a high-order numerical scheme by combining the Nystrom method in temporal direction with the compact finite difference method and the spectral method in spatial direction. The distinct advantage of this approach in comparison with most current methods is its high convergence rate even though the solution of the anomalous sub-diffusion equation usually has lower regularity on the starting point. The effectiveness and efficiency of our proposed method are verified by several numerical experiments.

math.NA↗

arXiv2017

Numerical algorithm for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term

In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is discussed, and the unconditional stability and convergence order of the numerical scheme are analysed. Finally, numerical experiments are carried out to verify the effectiveness and accuracy of the algorithm.

math.NA↗

arXiv2016

Maximum-norm error analysis of compact difference schemes for the backward fractional Feynman-Kac equation

The fractional Feynman-Kac equations describe the distribution of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the discretized schemes for fractional substantial derivatives proposed recently, we construct compact finite difference schemes for the backward fractional Feynman-Kac equation, which has q-th (q=1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. In the case q=1, the numerical stability and convergence of the difference scheme in the discrete L-infinity norm are proved strictly, where a new inner product is defined for the theoretical analysis. Finally, numerical examples are provided to verify the effectiveness and accuracy of the algorithms.

math.NA↗

arXiv2012

Control over stress induces plasticity of individual prefrontal cortical neurons: A conductance-based neural simulation

Behavioral control over stressful stimuli induces resilience to future conditions when control is lacking. The medial prefrontal cortex(mPFC) is a critically important brain region required for plasticity of stress resilience. We found that control over stress induces plasticity of the intrinsic voltage-gated conductances of pyramidal neurons in the PFC. To gain insight into the underlying biophysical mechanisms of this plasticity we used the conductance- based neural simulation software tool, NEURON, to model the increase in membrane excitability associated with resilience to stress. A ball and stick multicompartment conductance-based model was used to realistically fit passive and active data traces from prototypical pyramidal neurons in neurons in rats with control over tail shock stress and those lacking control. The results indicate that the plasticity of membrane excitability associated with control over stress can be attributed to an increase in Na+ and Ca2+ T-type conductances and an increase in the leak conductance. Using simulated dendritic synaptic inputs we observed an increase in excitatory postsynaptic summation and amplification resulting in elevated action potential output. This realistic simulation suggests that control over stress enhances the output of the PFC and offers specific testable hypotheses to guide future electrophysiological mechanistic studies in animal models of resilience and vulnerability to stress.

q-bio.NC↗