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Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation

Abstract

In this paper, we consider a boundary value problem (BVP) for a fourth-order nonlinear integro-differential equation. By reducing the problem to an operator equation, we establish the existence and uniqueness of the solution and construct a numerical method for solving it. We prove that the method is of second-order accuracy and obtain an estimate for the total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.

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Funding

This work is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant number 102.01-2021.03.

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Correspondence to Dang Quang A.

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Long, D.Q., A, D.Q. Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation. Numer Algor (2021). https://doi.org/10.1007/s11075-021-01198-3

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Keywords

  • Fourth-order nonlinear integro-differential equation
  • Existence and uniqueness of solution
  • Iterative method
  • Total error