Volterra type integral equation method for the radial Schrödinger equation: Single channel case
1
Citation
19
Reference
10
Related Paper
Citation Trend
Keywords:
Quadrature (astronomy)
In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.
Neumann series
Independent equation
Cite
Citations (2)
Quadrature (astronomy)
Cite
Citations (1)
This paper describes a one-step method based on the Lobatto four-point quadrature formula for the numerical solution of the differential equation [equation: see PDF] . The method has been extended to the linear differential equation [equation: see PDF] and to Volterra's linear integral equation of the second kind. In the case of ordinary linear second-order differential equation, a computational and theoretical comparison of the new method with other methods is also discussed.
Quadrature (astronomy)
Homogeneous differential equation
Universal differential equation
Cite
Citations (9)
В математических моделях физических явлений, использующих результаты экспериментов, зачастую возникает необходимость решения дифференциальных уравнений.Подобные задачи относятся к классу некорректных математических задач.В данной работе для получения приближенного решения дифференциального уравнения первого порядка с определенными краевыми условиями выполняется построение соответствующего регуляризирующего алгоритма.Реализуется метод, заключающийся в построении эквивалентного исходному дифференциальному урав
Volterra equations
Cite
Citations (1)
In this paper, we study the solvability of a second-kind Volterra integral equation. By replacing the right-hand side and the unknown function, the integral equation is reduced to an integral equation, the kernel of which is not «compressiblek. Using the Laplace transform, the obtained equation is reduced to an ordinary first-order differential equation (linear). Its solution is found. The solution of the homogeneous integral equation corresponding to the original nonhomogeneous integral equation found in explicit form. Special cases of a homogeneous integral equation and its solutions are written for different values of the parameter k. Classes are indicated in which the integral equation has a solution. Singular integral equations were considered in works [1–3]. Their kernels were also «incompressiblek, but kernels had an another form. In this connection, the weight classes of the solution existence differ from the class of the solution existence for the equation considered in this work.
Homogeneous differential equation
Integral transform
Cite
Citations (0)
Improper integral
Independent equation
Stratonovich integral
Cite
Citations (0)
Kernel (algebra)
Integral transform
Cite
Citations (2)
Quadrature (astronomy)
Spectral method
Cite
Citations (69)
This chapter describes the integral formulation of the equations of motion governing the vibration of continuous systems. An integral equation is an equation in which the unknown function appears under one or more signs of integration. If the unknown function appears nonlinearly in the regular and/or exceptional parts, the equation is said to be a nonlinear integral equation. Based on the type of integral in the regular part, the integral equations are classified as Fredholm- or Volterra-type equations. If the regular part of the integral equation contains a singular integral, the equation is called a singular integral equation. Otherwise, the equation is called a normal integral equation. Several methods, both exact and approximate methods, can be used to find the solutions of integral equations. The chapter considers the method of undetermined coefficients and the Rayleigh-Ritz, Galerkin, collocation, and numerical integration methods.
Cite
Citations (0)