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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A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme by Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis

“…The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. …”
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Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid by M. B. Akgül, G. Sarı, M. Pakdemirli

“…Adopting the obtained symmetry groups, governing partial differential equations are converted into ordinary differential equations and then solved numerically. …”
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On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs by F. N. Koumboulis, M. G. Skarpetis, B. G. Mertzios

“…The Euler equations, namely a set of nonlinear partial differential equations (PDEs), mathematically describing the dynamics of inviscid fluids are numerically integrated by directly modeling the original continuous-domain physical system by means of a discrete multidimensional passive (MD-passive) dynamic system, using principles of MD nonlinear digital filtering. …”
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A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method by R. Ellahi

“…Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. …”
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Vibration Suppression of a Coupled Aircraft Wing with Finite-Time Convergence by Yiming Liu, Zhifeng Tan, Xiaofen Yang, Xiaowei Wang

“…Since the model is modeled by partial differential equations, the traditional control design scheme based on the ordinary differential equation model is not applicable, and the control law design becomes very complex. …”
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On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients by Muhammad Mohsin, Syed Touqeer H. Shah, Ali A. Zaidi

“…In this paper, we study initial boundary value problems that involve functional (nonlocal) partial differential equations with variable coefficients. These problems arise in cell growth models with symmetric and asymmetric modes of division. …”
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On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation by Ghulam Yameen Mallah, Rajab Ali Malookani, Sajad Hussain Sandilo, Sanaullah Dehraj

“…The motion of axially moving beam in the term of transverse vibrations is expressed in the fourth-order linear and homogeneous partial differential equations with variable coefficients. The governing equations of motion are solved by using the two timescales perturbation method together with the Fourier expansion method. …”
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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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Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. …”
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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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Computer-Aided Numerical Inversion of Laplace Transform by Umesh Kumar

“…This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.…”
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Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model by Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei

“…The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. …”
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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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Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface by Atta Sojoudi, Ali Mazloomi, Suvash C. Saha, Y. T. Gu

“…The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. …”
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A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity by S. Shateyi, G. T. Marewo

“…A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. …”
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Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid by Norihan Md. Arifin, Roslinda Nazar, Ioan Pop

“…The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. …”
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On Modeling and Constrained Model Predictive Control of Open Irrigation Canals by Lihui Cen, Ziqiang Wu, Xiaofang Chen, Yanggui Zou, Shaohui Zhang

“…As a set of hyperbolic partial differential equations, they are not solved explicitly and difficult to design optimal control algorithms. …”
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A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations by E. H. Doha, D. Baleanu, A. H. Bhrawy, M. A. Abdelkawy

“…Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.…”
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New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation by Yu-Ming Chu, Shumaila Javeed, Dumitru Baleanu, Sidra Riaz, Hadi Rezazadeh

“…This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). …”
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