Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method by Shivaranjini S, Neetu Srivastava

“…Partial Differential Equations in Applied Mathematics…”
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Analyzing radiative heat on third-grade fluids over an expanding inclined sheet subject to higher-order chemical reaction: An overlapping grid spectral quasilinearization approach by Titilayo M Agbaje, Folarin Oluwaseun, S.R. Mishra, Rupa Baithalu, Subhajit Panda

“…Partial Differential Equations in Applied Mathematics…”
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A new finite difference algorithm for boundary value problems involving transmission conditions by Semih Çavuşoğlu, Oktay Sh. Mukhtarov

“…The finite difference method (FDM) is used to find an approximate solution to ordinary and partial differential equations of various type using finite difference equations to approximate derivatives. …”
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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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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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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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Solving arbitrary one-loop reduction via generating function by Tingfei Li, Yuekai Song, Liang Zhang

“…We first establish the partial differential equations governing the higher-pole generating function. …”
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Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules by Mohamed Rossafi, Roumaissae Eljazzar, Ram Mohapatra

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Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries by Bermúdez, Alfredo, Padín, Iago

“…For this purpose, advantage is taken from the fact that optimal control problems for stochastic ordinary differential equations (SDE) can be equivalently formulated as optimal control problems for deterministic partial differential equations (PDE), namely, the corresponding Fokker–Planck equation.…”
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Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, Pablo Alexei, Heid, Pascal, Süli, Endre

“…We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. …”
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Conciliating accuracy and efficiency to empower engineering based on performance: a short journey by Chinesta, Francisco, Cueto, Elias

“…The art of modeling for describing the behavior of complex systems from the solution of partial differential equations that are expected to govern their responses. …”
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Applying Fourier Neural Operator to insect wingbeat sound classification: Introducing CF-ResNet-1D by Béla J. Szekeres, Máté Natabara Gyöngyössy, János Botzheim

“…Despite recent advancements in Deep Learning, Fourier Neural Operators (FNO), efficient for solving Partial Differential Equations due to their global spectral representations, have yet to be thoroughly explored for real-world time series classification or regression tasks. …”
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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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Study on construction and identification of dynamic model of precooler in aviation bleed air system by SHI Zhouzheng, DONG Minghao, LIU Qi, LUO Ziyan, WANG Hongbo, QIN Xiansheng, WANG Zhanxi

“…The finite element method was used to establish the partial differential equation of the heat exchange mechanism, and the heat exchange mechanism of the precooler was analyzed. …”
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Analysis of non scalar control problems for parabolic systems by the block moment method by Boyer, Franck, Morancey, Morgan

“…We also deduce estimates on the cost of controllability when the final time goes to the minimal null control time.We illustrate how the method works on a few examples of such abstract controlled systems and then we deal with actual coupled systems of one dimensional parabolic partial differential equations. Our strategy enables us to tackle controllability issues that seem out of reach by existing techniques.…”
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New super and shock like solitary structures for KdV equation with higher-order nonlinearity by H.S. Alayachi, Abdulghani Alharbi, E.K. El-Shewy, Mahmoud A.E. Abdelrahman

“…The modified F-expansion approach is an effective, powerful and straightforward method for obtaining the solitary wave solutions to the nonlinear partial differential equations (NPDEs). The effect of model parameters on the nature, properties and structures of the model solutions have been examined. …”
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Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative by Attiya Nazneen, Rashid Nawaz, Laiq Zada, Nasir Ali, Mohamed Benghanem, Hijaz Ahmad

“…The method has been successfully applied to the higher dimension fractional order Partial differential equations and some fruitful results have been achieved. …”
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New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. …”
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Stochastic Diffusive Modeling of CO₂ Emissions with Population and Energy Dynamics by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Hisham M. Al-Khawar, Yasir Nawaz

“…A novel numerical scheme, an extension of the Euler-Maruyama algorithm, is proposed to solve stochastic time-dependent partial differential equations governing the model. The scheme's consistency and stability are rigorously analyzed in the mean square sense. …”
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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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