In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

Introduction: Head scans are the most frequently performed computed tomography (CT) examinations worldwide. However, there is growing concern over the probability of increased cancer risks among the exposed populations. Diagnostic reference levels (DRLs) identify radiation dose that is not commensurate with clinical objectives. The aim of this study was to establish DR...

This report describes the case of a 15-year-old male diagnosed with primary ALK-positive adenocarcinoma of the lung metastatic to the brain. He was treated with surgical resection for a single lesion followed by whole brain radiotherapy and subsequently underwent 10 courses of stereotactic radiosurgery for 47 lesions delivered over a four-year period. Currently, all metastatic lesions in the br...

A simple, consistent, semi-quantitative description of the neutron dose received by patients undergoing cancer treatment by X-ray therapy is given. This discussion is intended as a contribution to the AAPM Task Group on Neutrons from High-Energy X-Ray Machines. Submitted for Publication * Work supported'by the Department of Energy, contract DE-AC03-76SF00515.

BACKGROUND This study was designed to evaluate the integral dose (ID) received by normal tissue from intensity-modulated radiotherapy (IMRT) for prostate cancer. METHODS AND MATERIALS Twenty-five radiation treatment plans including IMRT using a conventional linac with both 6 MV (6MV-IMRT) and 20 MV (20MV-IMRT), as well as three-dimensional conformal radiotherapy (3DCRT) using 6 MV (6MV-3DCRT)...

Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

The radial and longitudinal distribution of absorbed dose in a water phantom irradiated with 10 GeV electrons has been measured. The electron beam was well focussed, and the current was measured accurately with a toroid. Detector plates, containing arrays of thermoluminescent 7LiF dosimeters were inserted at different depths in the water tank. The profiles of the dose distribution were measured...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...