New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions

A New Iterative Method For Solving Fuzzy Integral ‎Equations

In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are ‎valid.‎

Approximation of Solutions of the Forced Duffing Equation with Nonlocal Discontinuous Type Integral Boundary Conditions

Integral boundary conditions for evolution problems have various applications in chemical engineering, thermoelasticity, underground water flow and population dynamics, see for example [16, 17, 24]. In fact, boundary value problems involving integral boundary conditions have received considerable attention, see for instance, [3, 10], [12]–[15], [18, 19, 26] and the references therein. In a rece...

A New Method Based on the RKHSM for Solving Systems of Nonlinear IDDEs with Proportional Delays

and Applied Analysis 3 For any u(x) ∈ W 2 [0, +∞), let ⟨u(x), ψ i (x)⟩ = 0, i = 1, 2, . . ., which means that ⟨u (x) , (L ∗ φ i (x)⟩ = ⟨Lu (⋅) , φ i (⋅)⟩ = (Lu) (x i ) = 0. (12) Note that {x i } ∞ i=1 is dense in [0, +∞); therefore,Lu(x) = 0. It follows that u(x) ≡ 0 from the existence ofL. 3.1. Construction the of Iterative Sequence ?̃? n (x) and Ṽ n (x). Next we construct the iterative sequenc...

A new method for solving two-dimensional fuzzy Fredholm integral equations of the second kind

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

New iterative method for solving linear Fredholm fuzzy integral equations of the second kind