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...

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied...

Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature a weakly singular integral operator. Nevertheless, after a suitable periodization, the involved integral operator can be efficiently evaluated on trigonomet...

Keywords: Functional integral equation Existence Monotonic solutions Urysohn Compact in measure a b s t r a c t We study the existence of monotonic solutions for a perturbed functional integral equation of Urysohn type in the space of Lebesgue integrable functions on an unbounded interval. The technique associated with measures of noncompactness (in both the weak and the strong sense) and the D...

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

Mikhlin’s integral equation is a classical for solving boundary value problems Laplace’s equation. The kernel of the known as Neumann kernel. Recently, an Riemann–Hilbert problem was derived. new generalization kernel, and hence, it called generalized objective this paper to present detailed comparison between these two equations with emphasis on their similarities differences. This done throug...

Boundary integral methods for the solution of boundary value PDEs are an alternative to ‘interior’ methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution has singularities at these corners. In these cases, interior methods can become excessively expensive, as they require a finely discretised 2D mesh in the vici...

Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann-Schwinger (LS) equation is considered without invoking the traditional partial-wave decomposition. The singular kernel of the three-dimensional LS equation in coordinate space is regularized by a subtraction technique. The resulting nonsingular integral equation is then solved via the Nystro...