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A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems: 《Journal of Applied Mathematics and Physics》2024年第7期2559-2573,共15页Scott A. Sarra Derek Musgrave Marcus Stone Joseph I. Powell; Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with...; 关键词：Numerical Partial Differential Equations Boundary Value Problems Radial Basis Function Methods Ghost Points Variable Shape Parameter Least Squares

CONSERVATIVE CONFORMING AND NONCONFORMING VEMS FOR FOURTH ORDER NONLINEAR SCHRODINGER EQUATIONS WITH TRAPPED TERM: 《Journal of Computational Mathematics》2024年第2期454-499,共46页Meng Li Jikun Zhao Zhongchi Wang Shaochun Chen; supported by the NSF of China(Grant Nos.11801527,11701522,11771163,11671160,1191101330);by the China Postdoctoral Science Foundation(Grant No.2018M632791);by the Key Scientific Research Projects of Higher Eduction of Henan(Grant No.19A110034).; This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual...; 关键词：H^(2)conforming virtual element C^(0)nonconforming virtual element Morleytype nonconforming virtual element Nonlinear Schrodinger equation Conservation Convergence

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION被引量：1: 《Acta Mathematica Scientia》2024年第2期420-430,共11页向长林郑高峰; supported by the National Natural Science Foundation of China(12271296,12271195).; This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+...; 关键词：fourth order elliptic equation regularity theory Morrey space decay estimates Riesz potential

Bubbling solutions of fourth order mean field equations on S^(4): 《Science China Mathematics》2023年第6期1217-1236,共20页Changfeng Gui Yeyao Hu Weihong Xie; supported by National Science Foundation of USA (Grant No.DMS-1901914);supported by National Natural Science Foundation of China (Grant Nos.12101612 and 12171456)。; In this paper,we first establish the existence of blow-up solutions with two antipodal points of the fourth order mean field equations on S^(4).Moreover,we construct non-axially symmetric solutions with blow-up points...; 关键词：Paneitz operator bubbling solution axially symmetric solution non-axially symmetric solution regularpolyhedra

Higher Order Implicit Scheme for Nonlinear Time-Dependent Convection-Diffusion- Reaction Equation: 《American Journal of Computational Mathematics》2022年第2期232-248,共17页Uzair Ahmed Daoud Suleiman Mashat Dalal Adnan Maturi; A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a higher order numerical sc...; 关键词：Finite Difference Method (FDM) Crank-Nicholson (CN) Fourth Order Implicit (FOI) Convection-Diffusion-Reaction (CDR)

Analysis of Gray Scott’s Model Numerically: 《American Journal of Computational Mathematics》2021年第4期273-288,共16页Ahmed Abdulrahim Ahmed Amin Daoud Suleiman Mashat; In this paper, a two-dimensional nonlinear coupled Gray Scott system is simulated with a finite difference scheme and a finite volume technique. Pre and post-processing lead to a new solution called GSmFoam by underst...; 关键词：Fourth Order Compact Scheme Finite Volume Method Fully Implicit Scheme Alternating Direction Implicit (ADI) Scheme
Gray Scott Solver OPENFOAM

Stabilization for a Fourth Order Nonlinear Schrödinger Equation in Domains with Moving Boundaries: 《Journal of Partial Differential Equations》2021年第3期268-283,共16页VERA VILLAGRAN Octavio Paulo; partially financed by regular project Fondecyt 1191137.ANID.Chile.; In the present paper we study the well-posedness using the Galerkin method and the stabilization considering multiplier techniques for a fourth-order nonlinear Schrödinger equation in domains with moving boundaries.We...; 关键词：Nonlinear Schrödinger equation moving boundary STABILIZATION

High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes: 《Computer Modeling in Engineering & Sciences》2021年第8期699-715,共17页Luciano Pereira da Silva Bruno Benato Rutyna Aline Roberta Santos Righi Marcio Augusto Villela Pinto; In this article,we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes.The high order solutions obtained traditionally generate non-spar...; 关键词：Tenth order accuracy RRE compact scheme exponential scheme MULTIGRID finite difference

Studying the Impact of Vaccination Strategy and Key Parameters on Infectious Disease Models: 《Open Journal of Optimization》2020年第3期86-104,共19页Tahmineh Azizi Bacim Alali; In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international sp...; 关键词：Optimal Control S-I-R Model S-E-I-R Model LHS Monte Carlo Method Fourth Order Runge-Kutta

AN ERROR ANALYSIS METHOD SPP-BEAM AND A CONSTRUCTION GUIDELINE OF NONCONFORMING FINITE ELEMENTS FOR FOURTH ORDER ELLIPTIC PROBLEMS被引量：2: 《Journal of Computational Mathematics》2020年第1期195-222,共28页Jun Hu Shangyou Zhang; Under two hypotheses of nonconforming finite elements of fourth order elliptic problems,we present a side-patchwise projection based error analysis method(SPP-BEAM for short).Such a method is able to avoid both the re...; 关键词：Nonconforming finite element A priori error analysis Biharmonic equation

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