High-order collocation methods for nonlinear delay integral equation

Taylor collocation method for high-order neutral delay Volterra integro-differential equations

“…, k − 1} in the example 4.3 and 4.4. We compare our results with other well-known methods: the classical method [6], the Hermite method [13], the multistep method given in [12]. The results in these examples confirm the theoretical ones and suggest that the experimental order of convergence (EOC) is m (see EOC of example 4.1 and example 4.2 in Table 4.3).…”

“…Existence and uniqueness results for (1.1) can be easily proved by comparison with the theory for Volterra integral equations (see for example [6,11]). Equation (1.1) includes many important kinds of equations (see for example [4,6,12,13,15,18,25,29]) and this method can be used to obtain numerical solutions of high order differential equations (for {k 1,v } k−1 v=0 = {k 2,v } k−1 v=0 = {M v } k−1 v=0 = 0), high order integro-differential equations (for {k 2,v } k−1 v=0 = {M v } k−1 v=0 = 0), high order delay differential equation (for {k 1,v } k−1 v=0 = {k 2,v } k−1 v=0 = 0). There are many existing numerical methods for solving Volterra integrodifferential equations, such as Legendre spectral collocation method [26], Runge-Kutta method [7], spectral method [27,28], Polynomial collocation method [8][9][10]23], Tau method [14], operational matrices [2], Homotopy perturbation method [16,24], Haar wavelet method [21], Taylor polynomial [20,22].…”

Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review

“…We also underline that they have high uniform order, thus they do not suffer from the order reduction phenomenon, well-known in the ODEs context [9]. Other approaches, based on multistep collocation, have been proposed in [25][26][27][28][29][30][31][32].…”

Solution of the Systems of Delay Integral Equations in Heterogeneous Data Communication through Haar Wavelet Collocation Approach

“…Several researchers are trying to find out the numerical solution of delay IEs. Darania [6] used the multistep collocation method for solving DIEs. For each subinterval, the solution is obtained through a fixed number of collocation points and of previous steps in the current and next subintervals.…”