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On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels

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  • M. Basseem
  • Ahmad Alalyani

Abstract

All the previous authors discussed the quadratic equation only with continuous kernels by different methods. In this paper, we introduce a mixed nonlinear quadratic integral equation (MQNLIE) with singular kernel in a logarithmic form and Carleman type. An existence and uniqueness of MQNLIE are discussed. A quadrature method is applied to obtain a system of nonlinear integral equation (NLIE), and then the Toeplitz matrix method (TMM) and Nystrom method are used to have a nonlinear algebraic system (NLAS). The Newton–Raphson method is applied to solve the obtained NLAS. Some numerical examples are considered, and its estimated errors are computed, in each method, by using Maple 18 software.

Suggested Citation

  • M. Basseem & Ahmad Alalyani, 2020. "On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, November.
    • Handle: RePEc:hin:jnlmpe:7856207
    DOI: 10.1155/2020/7856207
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    Cited by:

    1. Ahmed M. A. El-Sayed & Eman M. A. Hamdallah & Malak M. S. Ba-Ali, 2022. "On the De Blasi Measure of Noncompactness and Solvability of a Delay Quadratic Functional Integro-Differential Equation," Mathematics, MDPI, vol. 10(9), pages 1-11, April.

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