MIM: A deep mixed residual method for solving high-order partial differential equations

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110930 ◽

2022 ◽

pp. 110930

Author(s):

Liyao Lyu ◽

Zhen Zhang ◽

Minxin Chen ◽

Jingrun Chen

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Partial Differential ◽

Residual Method

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On the solvability of nonlinear partial differential equations of a high order with deviating argument in lowest terms

Russian Mathematics ◽

10.3103/s1066369x16070021 ◽

2016 ◽

Vol 60 (7) ◽

pp. 7-13

Author(s):

O. I. Bzheumikhova ◽

V. N. Lesev

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Partial Differential ◽

Deviating Argument

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High order numerical algorithms based on biquadratic spline collocation for two-dimensional parabolic partial differential equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2018.1437260 ◽

2018 ◽

Vol 96 (3) ◽

pp. 500-536 ◽

Author(s):

Jun Liu ◽

Hui Guo ◽

Yao-Lin Jiang ◽

Yan Wang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Numerical Algorithms ◽

Parabolic Partial Differential Equations ◽

Two Dimensional ◽

Spline Collocation ◽

Partial Differential

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Lattice Boltzmann model for high-order nonlinear partial differential equations

Physical Review E ◽

10.1103/physreve.97.013304 ◽

2018 ◽

Vol 97 (1) ◽

Author(s):

Zhenhua Chai ◽

Nanzhong He ◽

Zhaoli Guo ◽

Baochang Shi

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Lattice Boltzmann ◽

Nonlinear Partial Differential Equations ◽

Lattice Boltzmann Model ◽

Partial Differential ◽

Boltzmann Model

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Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113298 ◽

2021 ◽

Vol 388 ◽

pp. 113298

Author(s):

Chaolong Jiang ◽

Yushun Wang ◽

Yuezheng Gong

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Partial Differential ◽

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Compactly supported radial basis functions for solving certain high order partial differential equations in 3D

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2014.11.012 ◽

2015 ◽

Vol 55 ◽

pp. 2-9 ◽

Author(s):

Wen Li ◽

Ming Li ◽

C.S. Chen ◽

Xiaofeng Liu

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Radial Basis Functions ◽

Basis Functions ◽

Partial Differential ◽

Compactly Supported ◽

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High-order finite element approximation for partial differential equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.01.012 ◽

2014 ◽

Vol 67 (4) ◽

pp. 709-711

Author(s):

Alexey Chernov ◽

Christoph Schwab

Keyword(s):

Finite Element ◽

Partial Differential Equations ◽

Differential Equations ◽

Finite Element Approximation ◽

Element Approximation ◽

Partial Differential

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Isogeometric Analysis and error estimates for high order partial differential equations in fluid dynamics

Computers & Fluids ◽

10.1016/j.compfluid.2014.07.002 ◽

2014 ◽

Vol 102 ◽

pp. 277-303 ◽

Author(s):

Anna Tagliabue ◽

Luca Dedè ◽

Alfio Quarteroni

Keyword(s):

Fluid Dynamics ◽

Partial Differential Equations ◽

Differential Equations ◽

Error Estimates ◽

Isogeometric Analysis ◽

Partial Differential

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Iterated Splitting Method of High Order for Time-Dependent Partial Differential Equations

SIAM Journal on Numerical Analysis ◽

10.1137/0721044 ◽

1984 ◽

Vol 21 (4) ◽

pp. 635-656 ◽

Author(s):

P. J. van der Houwen

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Splitting Method ◽

Time Dependent ◽

Partial Differential

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Application of functions of multidimensional matrices to the solution of systems of linear partial differential equations of high order

Ukrainian Mathematical Journal ◽

10.1007/bf01085474 ◽

1972 ◽

Vol 23 (4) ◽

pp. 415-424

Author(s):

N. P. Sokolov

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Multidimensional Matrices

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High-order finite element methods for time-fractional partial differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2011.01.011 ◽

2011 ◽

Vol 235 (11) ◽

pp. 3285-3290 ◽

Author(s):

Yingjun Jiang ◽

Jingtang Ma

Keyword(s):

Finite Element ◽

Partial Differential Equations ◽

Differential Equations ◽

Finite Element Methods ◽

Fractional Partial Differential Equations ◽

Partial Differential

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