Abstract
In this paper, we employ variational iterative method (VIM) to develop a suitable Algorithm for the numerical solution of systems of Volterra integro-differential equations. The formulated algorithm is used to solve first and second order linear and nonlinear system of Volterra integrodifferential equations which demonstrated a good numerical approach to overcome lengthen computational and integral simplification involves. Moreover, the comparison of the exact solution with the approximated solutions are made and approximate solutions p(x) q(t) proved to converge to the exact solutions p(x) q(t) respectively. The results reveal that the formulated algorithm are simple, effective and faster than analytical approach of solving Volterra integro-differential equations.
Highlights
Normal derivation has been an area of interest for many mathematicians and researchers their properties for example [1, 2]
T is a linear operator on a finite dimensional complex Hilbert space H, every commutator of the form AX — XA has trace 0 and 0 belongs to the numerical range W(AX-XA)
Has a local minimum at x in by Mecheri [9]. These results are on local minimum of the linear map in -classes [5]
Summary
Normal derivation has been an area of interest for many mathematicians and researchers their properties for example [1, 2]. As a Banach spaces K(H) can be identified with the dual of the ideal K of compact operators by means of the linear isometry of normal derivations. It was shown in Mecheri [9] that, if A is a unital C* Orc(A). The present paper initiates a study of the class D of operators A on H which have the property that 0 belongs to W(AX—XA)~ for every bounded operator X on H We call such operators finite, the term being suggested by the facts that D contains all normal operators, all compact operators, all operators having a direct summand of finite rank, and the entire C*-algebra generated by each of its members. The main focus in this paper is to study the local miminum and orthogonality in Cp-classes for normal derivations
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