In this paper, the computation of Hilbert singular integral with generalized composite Simpson's rule for is discussed. When singular points coincide with some a priori known point, the convergence rate of Simpson's rule higher than global one, we obtain the pointwise superconvergence phenomenon. ...
│ │ ├─IntegrationSimpsonRule │ │ └─IntersectingArea │ └─ equationSolving │ ├─LinearEquationSolvingProcess │ │ ├─ JacobisMethod │ │ └─ GaussSeidalMethod │ └─NonLinearEquationSolvingProcess ...
Using Simpson’s 3/8 rule, suitable average approximation and explicit backward Euler formula, we derive third order integration scheme in time which is L-stable. Present method provides accurate and stable results whenever inconsistencies are present in it for linear diffusion equation with Neumann ...
Simpson’s ruleThe functional equation of Pexider type f(x)-g(y)=(x-y)(h(x+y)+ψ(x)+φ(y)),x,y∈,(1) is shown to stem from Simpson's rule of integral calculus. The general solution of (1) may be described as follows: f is an arbitrary polynomial of fourth degree, g=f...
The L-stable Simpson-type rule (LSIMP3) obtained is then employed to derive a third-order time integration scheme for the diffusion equation. Numerical illustrations are provided to compare the performance of the new LSIMP3 scheme with the CrankNicolson scheme. While the CrankNicolson scheme can ...
This paper discusses the use of Product Simpson's rule to solve the integral equation eigenvalue problem lf(x)=貌1 1 k(|x y|)f(y)dy where k(t) = ln|t| or k(t) = t-a, 0 < a < 1, l, f and are unknowns which we wish to obtain. The function f(y) in the integral ...
In this paper, we introduce a novel approach to obtain approximate numerical solutions of linear Fredholm integral equations of the second kind. This method is founded on the modified Simpson's quadrature rule. We transform the Fredholm integral equation of the second kind into a ...