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A novel differential-integral quadrature method for the solution of nonlinear integro-differential equations
Faculty
Engineering
Year:
2021
Type of Publication:
ZU Hosted
Pages:
13945-13967
Authors:
Salwa Amien Mohamed ebrhiem
Staff Zu Site
Abstract In Staff Site
Journal:
Mathematical Methods in the Applied Sciences John Wiley & Sons Ltd
Volume:
Keywords :
, novel differential-integral quadrature method , , solution , nonlinear
Abstract:
In this work, we introduce an integration matrix operator that is fully consistent with the differentiation matrix operator defined by the differential quadrature method (DQM). Using these operators, a generic differential-integral quadrature method “DIQM” is proposed to directly discretize an integro-differential equation as a system of algebraic equations. To extend the applicability of the proposed DIQM to solve nonlinear and/or variable coefficients integrodifferential equation, some matrix manipulations are introduced. A stability analysis for Volterra integro-partial-differential equations is presented and the exponential convergence of the proposed method is examined. Various types of integro-differential equations are solved including ordinary/partial, linear/ nonlinear, Volterra parabolic/hyperbolic integro-differential equations with different boundary and initial conditions. Numerical results demonstrate the exponential convergence and the applicability of DIQM.
Author Related Publications
Salwa Amien Mohamed ebrhiem, "Thermal vibration characteristics of pre/post‑buckled bi‑directional functionally graded tapered microbeams based on modifed couple stress Reddy beam theory", Springer, 2020
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Salwa Amien Mohamed ebrhiem, "New Smoother to Enhance Multigrid-Based Methods for Bratu Problem", Elsevier, 2008
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Salwa Amien Mohamed ebrhiem, "Optimally efficient multigrid algorithms for incompressible Euler equations", Emerald Group Publishing Limited, 2008
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Salwa Amien Mohamed ebrhiem, "Adaptive FAS-multigrid method for nonlinear elliptic equations on unstructured grids", Wiley InterScience, 2007
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Department Related Publications
Amr Mohamed Salaheldeen Abdelaziem Mohamed, "Green’s function expansion for exponentially graded elasticity", لايوجد, 1900
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Hany Arafa Abdelmohsen Ali Metwallie, "Blended Learning Approach in Research and Education of Laboratory Physics", Conference ICL2010 September 15 -17, 2010 Hasselt, Belgium, 2010
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Magda Mahmoud Mohamed Kasem, "Group similarity solutions of (2 + 1) Boiti-Leon-Manna-Pempinelli Lax pair.", Elsvier, 2014
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Ola Ragab Abdou Mohamed, "Quadrature Analysis of Functionally Graded Materials", IJET-IJENS, 2014
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Mohamed Saad Metwaly Abdelkreem , "An Efficient Method to Solve Thermal Wave Equation", Scientific Research, 2014
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