Abstract
In this paper the use of the simple shooting-projection method for solving two-point boundary value problems for second-order ordinary integro-differential equations is proposed. Shooting methods are very suitable for solving such equations numerically, as the integral part of the equation can be evaluated while performing the shooting. The simple shooting-projection method consists of the following steps: First, a guess for the initial condition is made and a forward numerical integration is performed so that an initial value problem solution is obtained, called a shooting trajectory. The shooting trajectory satisfies the left boundary constraint but does not satisfy the right boundary constraint. Next, the shooting trajectory is transformed into a projection trajectory that is an approximate boundary value problem solution. Finally, from the projection trajectory a new initial condition is obtained and the procedure is repeated until convergence, i.e. until the boundary value problem solution is obtained within a prescribed precision.
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Filipov, S.M., Gospodinov, I.D., Angelova, J. (2015). Solving Two-Point Boundary Value Problems for Integro-Differential Equations Using the Simple Shooting-Projection Method. In: Dimov, I., Fidanova, S., Lirkov, I. (eds) Numerical Methods and Applications. NMA 2014. Lecture Notes in Computer Science(), vol 8962. Springer, Cham. https://doi.org/10.1007/978-3-319-15585-2_19
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DOI: https://doi.org/10.1007/978-3-319-15585-2_19
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