Results 11 to 20 of about 3,812 (235)

Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

International Journal of Mathematics and Mathematical Sciences, 2014
Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction
Nemat Dalir
doaj   +2 more sources

Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives [PDF]

Journal of Geometry and Physics, 2017
23 pages, no ...
Gorgone, Matteo, OLIVERI, Francesco
openaire   +5 more sources

Approximate Ad Hoc Parametric Solutions for Nonlinear First‐Order PDEs Governing Two‐Dimensional Steady Vector Fields [PDF]

Mathematical Problems in Engineering, 2010
Through a suitable ad hoc assumption, a nonlinear PDE governing a three‐dimensional weak, irrotational, steady vector field is reduced to a system of two nonlinear ODEs: the first of which corresponds to the two‐dimensional case, while the second involves also the third field component. By using several analytical tools as well as linear approximations
M. Markakis
openaire   +3 more sources

The upper–lower solution method for the coupled system of first order nonlinear PDEs

Journal of Mathematical Analysis and Applications, 2013
Abstract This paper is concerned with a coupled system of first order nonlinear partial differential equations. This system is, but not limited in, the extended case of the general blood–tissue exchange model (BTEX). We use the solutions of a coupled system of first order ordinary differential equations to construct a pair of ordered lower and upper ...
Guo-Chin Jau, Yu-Hsien Chang
openaire   +2 more sources

Adaptive-Growth Randomized Neural Networks for Level-Set Computation of Multivalued Nonlinear First-Order PDEs with Hyperbolic Characteristics

CoRR
This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics, including quasilinear hyperbolic balance laws and Hamilton--Jacobi equations.
Haoning Dang, Shi Jin, Fei Wang
openaire   +3 more sources

First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

Numerical Methods for Partial Differential Equations
ABSTRACTWe present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms.
N. Nguyen
openaire   +3 more sources

Efficient and accurate nonlinear model reduction via first-order empirical interpolation [PDF]

Journal of Computational Physics, 2023
We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs).
N. Nguyen, J. Peraire
semanticscholar   +1 more source

First-Order Conditions for the Optimal Control of Learning-Informed Nonsmooth PDEs [PDF]

Numerical Functional Analysis and Optimization, 2022
In this paper we study the optimal control of a class of semilinear elliptic partial differential equations which have nonlinear constituents that are only accessible by data and are approximated by nonsmooth ReLU neural networks.
Guozhi Dong, Michael Hintermüller, Kostas Papafitsoros, Kathrin Völkner   +3 more
semanticscholar   +1 more source

Adomian decomposition method for first order PDEs with unprescribed data

, 2021
In this paper we like to explore the full power of Adomian decomposition method (ADM), specially its symbolic capability. We will demonstrate the standard ADM and ADM with integration factor to compute explicit closed form solutions of first order scalar
T. Lu, Wei Zheng
semanticscholar   +1 more source

Exact solutions of classes of second order nonlinear partial differential equations reducible to first order

International Journal of Advances in Applied Sciences, 2023
This paper illustrates the successful implementation of the method of variation of parameters in combination with the method of characteristics and other techniques to obtain exact solutions for a wide range of partial differential equations.
Noureddine Mhadhbi, Sameh Gana, H. Alharbi   +2 more
semanticscholar   +1 more source