Discussion of (2+1) dimensional mixed integral equation with singular kernel
DOI:
https://doi.org/10.56405/dngcrj.2024.09.01.07Keywords:
Quadratic mixed integral equation(QMIE), Volterra Fredholm Integral equation, Banach FPT, Singular kerne, Chebyshev Polynomial, FPT (Fixed point theorem)Abstract
In this paper we discuss the uniqueness and existence of solution for a Quadratic Mixed Integral Equation (QMIE) on 2+1 dimensional in L2([0, a]×[0, b]×C[0, T]), (T < 1) space using fixed point theorem. Further we demonstrate convergence of the given existence result. Also we discuss the theoretical part of the Chybeshev polynomial method extending in 2+1 dimensional format and finally discuss the error analysis of the method.
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Abdel-Aty, M.A., Abdou, M.A., & Soliman, A.A. (2022). Solvability of quadratic integral equations with singular kernel. Journal of Contemporary Mathematical Analysis (Armenian Academy Of Sciences), 57 (1), 12-25.
Abusalim, S.M., Abdou, M.A., Nasr, M.E., & Abdel-Aty, M.A. (2023). An Algorithm for the Solution of Nonlinear Volterra-Fredholm Integral Equations with a Singular Kernel. Fractal and Fractional, 7 (10),730.
Al-Bugami, A.M., Abdou, M.A., & Mahdy, A.M.S. (2024). Numerical simulation, existence and uniqueness for solving nonlinear mixed partial integro-differential equations with discontinuous kernels. Journal of Applied Mathematics and Computing, 70, 5191-5211.
Al Hazmi, S.E. (2023). Projection-iterated method for solving numerically the nonlinear mixed integral equation in position and time. Journal of Umm Al-Qura University for Applied Sciences, 9 (2), 107-114.
Atkinson, K.E. (1997). The numerical solution of integral equations of the second kind. Cambridge University Press, Cambridge.
Alharbi, F.M. (2024). Stability Analysis of the Solution for the Mixed Integral Equation with Symmetric Kernel in Position and Time with Its Applications. Symmetry, 16 (8), 1048.
Alhazmi, S.E., Mahdy, A.M.S., Abdou, M.A., & Mohamed, D.S. (2023). Computational techniques for solving mixed (1+1) dimensional integral equations with strongly symmetric singular kernel. Symmetry, 15 (6), 1284.
Jan, A.R. (2022). Numerical solution via a singular mixed integral equation in (2+1) dimensional. Applied Mathematics & Information Sciences, 16 (6), 871-882.
Jan, A.R. (2022). An asymptotic model for solving mixed integral equation in position and time. Journal of Mathematics, Volume 2022, Article ID 8063971, 11 Pages.
Mahdy, A.M.S., Abdou, M.A., & Mohamed, D.S. (2024). A computational technique for computing second-type mixed integral equations with singular kernels. Journal of Mathematics and Computer Sciences, 32 (2), 137-151.
Mahdy, A.M.S., Abdou, M.A., & Mohamed, D.S., (2024). Numerical solution, convergence and stability of error to solve quadratic mixed integral equation. Journal of Applied Mathematics and Computing, 70, 5887-5916.
Mahdy, A.M.S., Abdou, M.A., Mohamed, D.S. (2023). Computational methods for solving higher-order (1+ 1) dimensional mixed-difference integro-differential equations with variable coefficients. Mathematics, 11 (9), 2045.
Matoog, R.T., Abdou, M.A., & Abdel-Aty, M.A. (2023). New algorithms for solving nonlinear mixed integral equations. AIMS Mathematics, 8 (11), 27488-27512.
Noeiaghdam, S., & Micula, S. (2021). A novel method for solving second kind Volterra integral equations with discontinuous kernel. Mathematics, 9 (17), 2172.
Wazwaz, A.M. (2011). Linear and nonlinear integral equations: Methods and applications, Springer Berlin, Heidelberg, 2011.
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