Special Issue "Numerical Methods for Differential and Integral Equations"

Deadline: 30 November 2019 (closed)
Guest Editors
Professor Şuayip Yüzbaşı, Department of Mathematics, Faculty of Science, Akdeniz University, Turkey
Professor Kamel Al-Khaled, Department of Mathematics, Jordan University of Science and Technology, Jordan
Professor Nurcan Baykuş Savaşaneril, Department of Mathematics, Faculty of Science, Dokuz Eylul University, Turkey
Professor Devendra Kumar, Department of Mathematics, University of Rajasthan, India


This special issue will focus on numerical solutions of diferential, integral and integro-differential equations, partial differential equations, fractional differential equations, fractional partial differential equations, stochastic partial differential equations and functional differential equations. The solutions of mentioned equations have a major role in many applied areas of science and engineering, For examle, physics, chemistry, astronomy, biology, mechanics, electronic, economics, potential theory, electrostatics. Since the mentioned equations are usually difficult to solve analytically, numerical methods are required. Therefore, this Special Issue will contribute to new numerical methods for solving the above mentioned equations and thus, many problems in science and engineering will be solved by means of new numerical methods in this special issue. We would like to invite researchers working on this topic to submit their articles to this Special Issue.

• Numerical methods for ordinary differential equations
• Numerical methods for delay differential equations
• Numerical methods for partial differential equations
• Numerical methods for fractional differential equations
• Numerical methods for integral equations
• Numerical methods for integro-differential equations
• Numerical methods for model problems of differential equations
• Numerical methods for fractional PDE
• Numerical methods for Stochastic PDE
• Numerical methods for functional differential equations

Published Papers
  • Modelling of Energy Storage Photonic Medium by WavelengthBased Multivariable Second-Order Differential Equation
  • Abstract Wavelength-dependent mathematical modelling of the differential energy change of a photon has been performed inside a proposed hypothetical optical medium. The existence of this medium demands certain mathematical constraints, which have been derived in detail. Using reverse modelling, a medium satisfying the derived conditions is proven to store energy as the photon propagates from the entry to exit point. A single photon with a given intensity is considered in the analysis and hypothesized to possess a definite non-zero probability of maintaining its energy and velocity functions analytic inside the proposed optical medium, despite scattering, absorption, fluorescence, heat generation, and other… More
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  • On Caputo-Type Cable Equation: Analysis and Computation
  • Abstract In this paper, a special case of nonlinear time fractional cable equation is studied. For the equation defined on a bounded domain, the existence, uniqueness, and regularity of the solution are firstly studied. Furthermore, it is numerically studied via the weighted and shifted Grünwald difference (WSGD) methods/the local discontinuous Galerkin (LDG) finite element methods. The derived numerical scheme has been proved to be stable and convergent with order O(∆t2 + hk+1), where ∆t, h, k are the time stepsize, the spatial stepsize, and the degree of piecewise polynomials, respectively. Finally, a numerical experiment is presented to verify the theoretical analysis. More
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  • Fractional Analysis of Viscous Fluid Flow with Heat and Mass Transfer Over a Flexible Rotating Disk
  • Abstract An unsteady viscous fluid flow with Dufour and Soret effect, which results in heat and mass transfer due to upward and downward motion of flexible rotating disk, has been studied. The upward or downward motion of non rotating disk results in two dimensional flow, while the vertical action and rotation of the disk results in three dimensional flow. By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations. The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables. Then, we generalize the model by using… More
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  • Integral Transform Method for a Porous Slider with Magnetic Field and Velocity Slip
  • Abstract Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag. There is a slip-on both the slider and the ground in the two cases, for example, a long porous slider and a circular porous slider. By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method. Solutions are obtained for different values of Reynolds numbers, velocity slip, and magnetic field. We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long… More
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  • Analytical and Numerical Investigation for the DMBBM Equation
  • Abstract The nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation is solved numerically using adaptive moving mesh PDEs (MMPDEs) method. Indeed, the exact solution of the DMBBM equation is obtained by using the extended Jacobian elliptic function expansion method. The current methods give a wider applicability for handling nonlinear wave equations in engineering and mathematical physics. The adaptive moving mesh method is compared with exact solution by numerical examples, where the explicit solutions are known. The numerical results verify the accuracy of the proposed method. More
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