Representation formula for solution of a functional equation with Volterra operator
نویسندگان
چکیده
منابع مشابه
Application of the block backward differential formula for numerical solution of Volterra integro-differential equations
In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...
متن کاملSolution of a tridiagonal operator equation
Let H be a separable Hilbert space with an orthonormal basis {en/n ∈ N}, T be a bounded tridiagonal operator on H and Tn be its truncation on span ({e1, e2, . . . , en}). We study the operator equation T x = y through its finite dimensional truncations Tnx = yn. It is shown that if {‖T−1 n en‖} and {‖T ∗−1 n en‖} are bounded, then T is invertible and the solution of T x = y can be obtained as a...
متن کاملApproximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel
M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, On the numerical solutions of Fredholm-Volterra integral equation, Appl. Math. Comp. 146, 713-728, (2003). M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, Toeplitz Matrix and product Nystrom methods for solving the singular integral equation, Le Matematiche LVII-Fasc. I, 21-37, (2002). H. Brunner, On the numerical solution of nonlinear VolterraF...
متن کاملNumerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method
In this paper, a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method. In this method, a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution. Error analysis of this method is also ...
متن کاملPseudodifferential Multi-product Representation of the Solution Operator of a Parabolic Equation
By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on Rn as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.03.026