Integral Equations

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Jiongmin Yong - One of the best experts on this subject based on the ideXlab platform.

  • mean field backward stochastic volterra Integral Equations
    Discrete and Continuous Dynamical Systems-series B, 2013
    Co-Authors: Yufeng Shi, Tianxiao Wang, Jiongmin Yong
    Abstract:

    Mean-field backward stochastic Volterra Integral Equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted M-solutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra Integral Equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. A Pontryagin's type maximum principle is established for an optimal control of MF-FSVIEs.

  • mean field backward stochastic volterra Integral Equations
    arXiv: Probability, 2011
    Co-Authors: Yufeng Shi, Tianxiao Wang, Jiongmin Yong
    Abstract:

    Mean-field backward stochastic Volterra Integral Equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted M-solutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra Integral Equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. As applications, a multi-dimensional comparison theorem is proved for adapted M-solutions of MF-BSVIEs and a maximum principle is established for an optimal control of MF-FSVIEs.

  • well posedness and regularity of backward stochastic volterra Integral Equations
    Probability Theory and Related Fields, 2008
    Co-Authors: Jiongmin Yong
    Abstract:

    Backward stochastic Volterra Integral Equations (BSVIEs, for short) are studied. Notion of adapted M-solution is introduced. Well-posedness of BSVIEs is established and some regularity results are proved for the adapted M-solutions via Malliavin calculus. A Pontryagin type maximum principle is presented for optimal controls of stochastic Volterra Integral Equations.

Abdulmajid Wazwaz - One of the best experts on this subject based on the ideXlab platform.

  • linear and nonlinear Integral Equations methods and applications
    2011
    Co-Authors: Abdulmajid Wazwaz
    Abstract:

    Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear Integral Equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear Integral Equations. The Volterra Integral and integro-differential Equations, the Fredholm Integral and integro-differential Equations, the Volterra-Fredholm Integral Equations, singular and weakly singular Integral Equations, and systems of these Equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear Integral Equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Pad approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.

  • Systems of Singular Integral Equations
    Linear and Nonlinear Integral Equations, 2011
    Co-Authors: Abdulmajid Wazwaz
    Abstract:

    Systems of singular Integral Equations appear in many branches of scientific fields [1–6], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Studies of systems of singular Integral Equations have attracted much concern in applied sciences. The use of computer symbolic systems such as Maple and Mathematica facilitates the tedious work of computation. The general ideas and the essential features of these systems are of wide applicability.

  • The modified decomposition method for analytic treatment of non-linear Integral Equations and systems of non-linear Integral Equations
    International Journal of Computer Mathematics, 2005
    Co-Authors: Abdulmajid Wazwaz
    Abstract:

    We demonstrate the use of the modified decomposition method for the analytic treatment of non-linear Fredholm Integral Equations, non-linear Volterra Integral Equations and systems of non-linear Integral Equations. The proper implementation of the modified method can dramatically reduce the amount of work required and may provide the exact solution using only a few iterations. The analysis is accompanied by numerical illustrations that show the pertinent features of the technique.

  • a first course in Integral Equations
    1997
    Co-Authors: Abdulmajid Wazwaz
    Abstract:

    Classifications of Integral Equations Fredholm Integral Equations Volterra Integral Equations Fredholm Integro-Differential Equations Volterra Integro-Differential Equations Singular Integral Equations Nonlinear Fredholm Integral Equations Nonlinear Volterra Integral Equations Applications of Integral Equations

Juan J. Trujillo - One of the best experts on this subject based on the ideXlab platform.

E.g. Ladopoulos - One of the best experts on this subject based on the ideXlab platform.

  • singular Integral Equations linear and non linear theory and its applications in science and engineering
    2000
    Co-Authors: E.g. Ladopoulos
    Abstract:

    1 - Introduction.- 2 - Finite-Part Singular Integral Equations.- 3 - Finite-Part Singular Integral Equations in Elasticity and Fracture Mechanics.- 4 - Singular Integral Equations in Aerodynamics.- 5 - Multidimensional Singular Integral Equations.- 6 - Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Isotropic Solids.- 7 - Multidimensional Singular Integral Equations in Relativistic Elastic Stress Analysis for Moving Frames.- 8 - Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Anisotropic Solids.- 9 - Multidimensional Singular Integral Equations in Plasticity of Isotropic Solids.- 10 - Non-Linear Singular Integral Equations.- 11 - Numerical Evaluation Methods for Non-Linear Singular Integral Equations.- 12 - Non-Linear Singular Integral Equations in Fluid Mechanics.- 13 - Non-Linear Integro-Differential Equations in Structural Analysis.- 14 - Non-Linear Singular Integral Equations in Elastodynamics.- 15 - Conclusions.- Appendix - Mathematical Definitions.- Author Index.

  • Finite-Part Singular Integral Equations
    Singular Integral Equations, 2000
    Co-Authors: E.g. Ladopoulos
    Abstract:

    Finite-part singular Integral Equations are recently widely applicable in many important problems of engineering mechanics, like elasticity, plasticity, fracture mechanics and aerodynamics. The general property of this type of singular Integral Equations, consists to the generalization of the Cauchy singular Integral Equations, which have been systematically studied during the last decades.

  • Singular Integral Equations in Aerodynamics
    Singular Integral Equations, 2000
    Co-Authors: E.g. Ladopoulos
    Abstract:

    Finite-part singular Integral Equations are further widely applicable in other important problems of engineering mechanics, like aerodynamics. Hence, it is of interest to solve numerically the systems of the singular Integral Equations of the respective boundary value problem, instead of the problem itself.

  • Non-Linear Singular Integral Equations
    Singular Integral Equations, 2000
    Co-Authors: E.g. Ladopoulos
    Abstract:

    Many problems of engineering mechanics, like structural analysis and fluid mechanics, reduce to the solution of a non-linear singular Integral equation. Hence, there is an increasing interest to the solution of such non-linear Integral Equations, since these are connected with a wide range of problems of an applied character. The theory of non-linear singular Integral Equations seems to be particularly complicated if closely linked with applied mechanics problems.

  • Non-Linear Singular Integral Equations in Elastodynamics
    Singular Integral Equations, 2000
    Co-Authors: E.g. Ladopoulos
    Abstract:

    Applications of the non-linear singular Integral Equations are further given to other aspects of applied science and engineering, like elastodynamics. Therefore, a seismic wave Equations analysis is investigated, by reducing the problem to the solution of a non-linear singular Integral equation.

Salih Yalcinbas - One of the best experts on this subject based on the ideXlab platform.

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