Interval differential equations with a second type Hukuhara derivative

Random Set–valued Functional Differential Equations with the Second Type Hukuhara Derivative

This paper concerns with the initial value problem for random set-valued functional differential equations with the second type Hukuhara derivative (RSFDEs). By using the techniques of successive approximations, the existence and uniqueness of solutions are established. Two kinds of boundedness of the solution are also established. In addition, the problem at least one solution under some condi...

Numerical Solution of Interval Differential Equations with Generalized Hukuhara Differentiability

A Gautschi-type method for oscillatory second-order differential equations

We study a numerical method for second-order differential equations in which high-frequency oscillations are generated by a linear part. For example, semilinear wave equations are of this type. The numerical scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly. We prove that the method admits secondorder error bounds which are independent of the ...

P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations

Some new higher algebraic order symmetric various-step methods are introduced. For these methods a direct formula for the computation of the phase-lag is given. Basing on this formula, calculation of free parameters is performed to minimize the phase-lag. An explicit symmetric multistep method is presented. This method is of higher algebraic order and is fitted both exponentially and trigonomet...

Combined compact difference scheme for linear second-order partial differential equations with mixed derivative

A combined compact difference scheme is proposed for linear second-order partial differential equations with mixed derivative. The scheme is based on a nine-point stencil at interior with sixth-order accurate local truncation error. Fourier analysis is used to analyze the spectral resolution of the proposed scheme. Numerical tests demonstrate at least sixth-order convergence rate with Dirichlet...