Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation by Fazle Mabood, Stanford Shateyi

“…Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. …”
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High-Order Compact Implicit Difference Methods For Parabolic Equations in Geodynamo Simulation by Don Liu, Weijia Kuang, Andrew Tangborn

“…A series of compact implicit schemes of fourth and sixth orders are developed for solving differential equations involved in geodynamics simulations. …”
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Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications by Veli Shakhmurov

“…The infinite systems of the degenerate partial differential equations and Cauchy problem for system of parabolic equations are further studied in applications.…”
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Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.…”
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Quasilinear Hyperbolic Systems Applied to Describe the Magnetohydrodynamic Nanofluid Flow by Dayong Nie

“…The influence of velocity slip on the flow and heat transfer properties of a hyperbolic nanofluid has been investigated. The partial differential equations for nanoparticle solid concentration, energy, and motion were turned into ordinary differential equations. …”
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Periodic Problems of Difference Equations and Ergodic Theory by B. A. Biletskyi, A. A. Boichuk, A. A. Pokutnyi

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Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method by Salem Alkhalaf

“…It is observed that the method is easy to implement and quite valuable for handling nonlinear system of partial differential equations and yielding excellent results at minimum computational cost. …”
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Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation by Andrew Gratien Johnpillai, Chaudry Masood Khalique

“…These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. …”
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Evaluating a family of two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence by R. Bonciani, V. Del Duca, H. Frellesvig, J.M. Henn, M. Hidding, L. Maestri, F. Moriello, G. Salvatori, V.A. Smirnov

“…The computation of the integrals is performed with the method of differential equations. We provide a choice of basis for the polylogarithmic sectors, that puts the system of differential equations in canonical form. …”
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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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ESTABLISHED MODES AND STATIC CHARACTERISTICS OF THREE-PHASE ASYNCHRONOUS MOTOR POWERED WITH SINGLE PHASE NETWORK by V. S. Malyar, V. V. Malyar

“…In order to perform it, the original nonlinear differential equations are algebraized by approximating the variables with the use of cubic splines. …”
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VIM for Solving the Pollution Problem of a System of Lakes by J. Biazar, M. Shahbala, H. Ebrahimi

“…Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. …”
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Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature by Asma Khalid, Ilyas Khan, Sharidan Shafie

“…The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. …”
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Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions by Xin-You Meng, Li Xiao

“…Furthermore, due to the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the model is investigated by considering time delay as the bifurcation parameter. …”
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An Exact Solution of the Binary Singular Problem by Baiqing Sun, Kun Tang, Hongmei Zhang, Shan Xiong

“…Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. …”
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Self-organization through decoupling by Romar Correa

“…On the other hand, we provide a theorem showing that a coupled set of differential equations can become uncoupled and vice versa as an argument in favour of the second thesis. …”
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Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows by M. M. Potsane, R. J. Moitsheki

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Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme by Zhaofeng An, Suxia Zhang, Jinhu Xu

“…In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. …”
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Travelling wave solutions to some PDEs of mathematical physics by Kourosh Nozari, Ghasem Alizadeh Afrouzi

“…As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity and multifluid flows, or some new cosmological models such as signature changing space-times. …”
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Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models by Jingwen Zhang

“…The first application of a technique for solving Volterra integro-differential equations of the fuzzy type, which was devised and tested in this paper, is shown here. …”
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