On expansions for nonlinear systems Error estimates and convergence issues by Beauchard, Karine, Le Borgne, Jérémy, Marbach, Frédéric

“…Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. …”
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Chemical reaction and Soret impacts on MHD heat and mass transfer Casson hybrid nanofluid (MoS2+ZnO) flow based on engine oil across a stretching sheet with radiation by M. Radhika, Y. Dharmendar Reddy

“…The relevant similarity variables convert the governing nonlinear partial differential equations to ordinary differential equations (ODEs). …”
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Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops by F. Moriello

“…This is achieved by defining differential equations along contours connecting two fixed points, and by solving them in terms of one-dimensional generalised power series. …”
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The general solutions of difference vector-equations with constant coefficients by Artūras Štikonas

“…We find the simple formulae between solution of the first order homogeneous differential equations and solution of difference equation. …”
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Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. by Byonaneebye, Darius

“…The Dormand-Prince method is a technique similar to the Runge-Kutta method for solving ordinary differential equations (ODEs). It uses six function evaluations to compute solutions with fourth and fifth-order accuracy. …”
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Substantiation of asymptotical solution of weakly nonlinear hyperbolic system by Aleksandras Krylovas

“… A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. …”
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Existence Results for an Implicit Coupled System Involving $\xi$-Caputo and $p$-Laplacian Operators by Walid Benhadda, Abderrazak Kassidi, Ali El Mfadel, Elomari M'hamed

“…This paper aims to establish the existence and uniqueness of a solution to a coupled system of $\xi$-Caputo fractional differential equations involving the $p$-Laplacian operator in an arbitrary Banach space. …”
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Computational analysis of bioconvective MHD hybrid nanofluid flow of non-Newtonian fluid over cone/plate: A study based on the Cattaneo-Christov heat and mass flux model by P. Francis, P. Sambath, S. Noeiaghdam, U. Fernandez-Gamiz, S. Dinarvand

“…A similarity transformation is used to simplify the complex partial differential equations into ordinary differential equations, which are then solved using the Keller Box finite difference method. …”
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Calculation of pipe bend and tension in case of fluid velocity pulsation by Rimantas Didžgalvis, Antanas Sudintas, Irena Tiknevičienė

“… The mathematical model of a bend pipe with a flowing fluid at a fluid pulsation was created. By solving differential equations, an analytical expression of solution is received, which may be well used for calculation of normal tension of the pipe at different ground load quantities and flow velocity pulsation. …”
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Calculation of bending deflection and stresses of a pipe with flowing fluid in the case of variable ground load by Rimantas Didžgalvis, Antanas Sudintas, Irena Tiknevičienė

“…Using the methods of approximate solutions of differential equations, the analytical pipe bend dynamic expressions were given at the case, when the ground load minimises expo­nentially. …”
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Integral invariant manifold method applied to a mathematical model of osteosarcoma by Ophir Nave

“…These interactions are described by nonlinear ordinary differential equations. By applying the MIM method, two critical dynamic variables (Cancer cells and Necrotic cells) were identified, providing insights into the dynamics of osteosarcoma over time during treatment.…”
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Gluing for the Einstein constraint equations by Corvino, Justin

“…Initial data for the Einstein equations must satisfy a system of nonlinear partial differential equations, the Einstein constraint equations. …”
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Existence Analysis of Multi-Point Boundary Value Problems with Riesz-Caputo Fractional Derivatives by Takieddine Zeghida, Rabah Khaldi, Assia Guezane-Lakoud

“…This paper explores the study of a specific category of nonlinear multi-point boundary value problems (BVPs) associated with Riesz-Caputo fractional differential equations and integral boundary conditions. The primary objective is to establish the existence of solutions under specific assumptions. …”
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Mathematical Modeling of Commensalism Between Two Species with Limited Resources. by Namutebi, Aminah

“…This model is characterized by a pair of first-order non-linear coupled differential equations. All four equilibrium points of the model are identified and the nature of stability of the four equilibrium points is discussed using the Jacobian and trace determinant method. …”
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A Mathematical Model For The Population Dynamics Of Disease Transmiting Vectors in Particular Female Anopheles Mosquitoes. by Turyamusiima, Richard

“…The mosquito free equilibrium and endemic equilibrium have been determined by setting system of ordinary differential equations to zero. Basic reproduction has been determined using the next generation matrix management analyzed. …”
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Thermal radiation and thermo-diffusion in Casson-ferrofluid over a magnetized porous surface: RSM analysis by S. Manjunatha, J. Santhosh Kumar, Khalil Ur Rehman, Wasfi Shatanawi, S.V.K. Varma

“…Similarity transformations convert the flow model's governing nonlinear coupled partial differential equations into ordinary coupled differential equations. …”
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Some new existence results of positive solutions for anisotropic variable exponent operator by Rafik Guefaifia, Salah Boulaaras, Rashid Jan

“…By deriving new existence results, the study advances the understanding of nonlinear partial differential equations in anisotropic and variable exponent settings. …”
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Mathematical Modelling of the Transmission of Malaria. by Atubangire, Felix

“…The model takes in the ordinally differential equations. The basic reproduction number Ro is obtained. …”
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Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity by Keimer, Alexander, Pflug, Lukas

“…This fixed-point problem itself necessitates the study of existence, uniqueness and stability of a class of discontinuous ordinary differential equations. On the ODE level, we compare the solution type defined here with the well-known Carathéodory and Filippov solutions.…”
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$\phi $-FEM for the heat equation: optimal convergence on unfitted meshes in space by Duprez, Michel, Lleras, Vanessa, Lozinski, Alexei, Vuillemot, Killian

“…Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh, not fitting the domain and its real boundary exactly. …”
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