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A computational method for numerically solving linear integro-differential equations

Saeed Hatamzadeh-Varmazyar, Zahra Masouri


A special representation of vector forms of triangular functions (TFs) is used for formulation of an efficient direct method for numerical solution of linear Volterra and Fredholm integrodifferential equations. Using this approach, an integro-differential equation reduces to a linear system of algebraic equations. No integration is needed for setting up the system and, therefore, all calculations can easily be implemented. Moreover, no projection method such as collocation, Galerkin, and so on, is used for implementation of this approach which leads to a lower computational cost. Some test problems are provided to illustrate that the method is practical and has a good accuracy.


Integro-differential equations, Direct method, Vector forms, Triangular functions, Operational matrix of integration.

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