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Article
A Fast Sine Transform Accelerated High-Order Finite Difference Method for Parabolic Problems over Irregular Domains
In this paper, a new Cartesian grid finite difference scheme is introduced for solving parabolic initial-boundary value problems involving irregular domains and Robin boundary condition in two and three dimens...
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Article
Open AccessCuproptosis correlates with immunosuppressive tumor microenvironment based on pan-cancer multiomics and single-cell sequencing analysis
Recent studies suggest that cuproptosis, a novel mode of cell death, may be associated with the development of cancer. However, no studies are showing its role in tumorigenesis, progression, and prognosis. In ...
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Article
Richardson extrapolation method for 2D-SPP on VB mesh singularly perturbed convection–diffusion problem on a Vulanović–Bakhvalov mesh
This paper discusses the Richardson extrapolation technique of an upwind finite difference scheme on a modified Bakhvalov-type mesh (named Vulanović–Bakhvalov mesh) for a model singularly perturbed convection–...
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Article
A novel parameter-uniform numerical method for a singularly perturbed Volterra integro-differential equation
A novel parameter-uniform finite difference scheme on a Shishkin-type mesh for a singularly perturbed Volterra integro-differential equation is studied. The problem is discretized by the variable two-step back...
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Article
Comprehensive multi-omics analysis of the m7G in pan-cancer from the perspective of predictive, preventive, and personalized medicine
The N7-methylguanosine modification (m7G) of the 5′ cap structure in the mRNA plays a crucial role in gene expression. However, the relation between m7G and tumor immune remains unclear. Hence, we intended to ...
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Article
Multilevel augmentation methods for eigen-problems of compact integral operators
In this paper, we combine the ideas of multilevel augmentation methods for solving integral equations and the shifted-inverse power method to develop a new multilevel augmentation method for solving eigen-prob...
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Article
FFT-Based High Order Central Difference Schemes for Poisson’s Equation with Staggered Boundaries
This work concerns with the development of fast and high order algorithms for solving a single variable Poisson’s equation with rectangular domains and uniform meshes, but involving staggered boundaries. Here ...
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Article
A robust adaptive grid method for a nonlinear singularly perturbed differential equation with integral boundary condition
In this paper, the numerical solution of a nonlinear first-order singularly perturbed differential equation with integral boundary condition is considered. The discrete method is generated by a backward Euler ...
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Article
Estimating spatial pattern of hyporheic water exchange in slack water pool
Hyporheic zone (HZ) influences hydraulic and biogeochemical processes in and alongside streams, therefore, investigating the controlling geographic factors is beneficial for understanding the hydrological proc...
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Article
Open AccessParameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations
In this paper, we propose a numerical scheme for a system of two linear singularly perturbed parabolic convection-diffusion equations. The presented numerical scheme consists of a classical backward-Euler sche...
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Article
Analysis of the SDFEM for singularly perturbed differential–difference equations
In this paper, the stability and accuracy of a streamline diffusion finite element method (SDFEM) for the singularly perturbed differential–difference equation of convection term with a small shift is consider...
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Article
B-spline collocation and self-adapting differential evolution (jDE) algorithm for a singularly perturbed convection–diffusion problem
Many numerical methods applied on a Shishkin mesh are very popular in solving the singularly perturbed problems. However, few approaches are used to obtain the Shishkin mesh transition parameter. Thus, in this...
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Chapter and Conference Paper
Numerical Solution of Singularly Perturbed Convection Delay Problems Using Self-adaptive Differential Evolution Algorithm
In this paper, a new numerical technique is constructed to solve singularly perturbed convection delay problems. First of all, based on Taylor’s series expansion, the given problem is transformed into a singul...
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Article
Investigating spatial variability of vertical water fluxes through the streambed in distinctive stream morphologies using temperature and head data
Investigating the interaction of groundwater and surface water is key to understanding the hyporheic processes. The vertical water fluxes through a streambed were determined using Darcian flux calculations and...
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Article
Heterogeneity of hydraulic conductivity and Darcian flux in the submerged streambed and adjacent exposed stream bank of the Beiluo River, northwest China
Recognizing the heterogeneity of hydraulic conductivity and hyporheic flow is critical for understanding contaminant transfer and biogeochemical and hydrological processes involving streams and aquifers. In th...
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Article
Legendre Spectral Projection Methods for Fredholm–Hammerstein Integral Equations
In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Hammerstein integral equation. The convergence of the approximate solutions to...
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Article
Erratum: Spatial variability of streambed vertical hydraulic conductivity and its relation to distinctive stream morphologies in the Beiluo River, Shaanxi Province, China
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Article
Spatial variability of streambed vertical hydraulic conductivity and its relation to distinctive stream morphologies in the Beiluo River, Shaanxi Province, China
Streambed vertical hydraulic conductivity (K v) is a key parameter in the analysis of interactions between streams and aquifers, and of stream ecosystems. However, knowledge of the streamb...
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Article
Iterated Fast Collocation Methods for Integral Equations of the Second Kind
In this paper a new iteration technique is proposed based on fast multiscale collocation methods of Chen et al. (SIAM J Numer Anal 40:344–375, 2002) for Fredholm integral equations of the second kind. It is shown...
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Article
A fast multiscale Kantorovich method for weakly singular integral equations
In this paper, we use the idea of Kantorovich regularization to develop the fast multiscale Kantorovich method and the fast iterated multiscale Kantorovich method. For some kinds of weakly singular integral eq...
