Numerical solution and dynamical studies for (2 + 1) dimensional Volterra–Fredholm integral equations with a discontinuous kernel

Faculty Science Year: 2025
Type of Publication: ZU Hosted Pages: 3671–3697
Authors:
Doaa Shoukry Mohamed Abdulmutallab
Journal: Journal of Applied Mathematics and Computing Springer Volume:
Keywords : Numerical solution , dynamical studies , , , 1) dimensional Volterra–Fredholm    
Abstract:
In this paper, using the space L2([a, b] × [c, d]) × C[0, T ], (T < 1), we have introduced a new and efficient approach to a discontinuous kernel solution of (2 + 1) dimensional mixed Volterra–Fredholm integral equations (MVFIE). By applying the separation of variables approach, the (2 + 1) dimensional MVFIE has been reduced to a two-dimensional Fredholm integral Eq. (2D-FIE). Next, we derive a system of linear algebraic equations using the Chebyshev polynomials of the sixth-kind (CP6K) approach.We are demonstrating that the integral equations solution exists and unique. Convergence of solutions has been proven. Numerical simulations have been given to verify that the new method produces more efficient and better results. The error in each example is computed by using Maple software.
    
     
 
       

Author Related Publications

  • Doaa Shoukry Mohamed Abdulmutallab , "Fractional Calculus for Solving generalized Abel’s Integral Equations using Chebyshev Polynomials", Foundation of Computer Science, 2014 More
  • Doaa Shoukry Mohamed Abdulmutallab , "Numerical solution of singular and non singular integral equations", Brazil Departamento de Matemática, Universidade Federal de Pernambuco, CEP 50740-540, Recife-PE, 2013 More
  • Doaa Shoukry Mohamed Abdulmutallab , "Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial", Hindawi Publishing Corporation, 2014 More
  • Doaa Shoukry Mohamed Abdulmutallab , "NUMERICAL SOLUTION OF FRACTIONAL SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS BY USING TAYLOR SERIES EXPANSION AND GALERKIN METHOD", 2014 Scientific Advances Publishers, 2014 More
  • Doaa Shoukry Mohamed Abdulmutallab , "NONLINEAR SINGULAR INTEGRAL EQUATIONS WITH SHIFT IN THE GENERALIZED HÖLDER SPACES", USA.EUDOXUS PRESS,LLC, 2010 More

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