The adapted block boundary value methods for singular initial value problems

Wang, Huiru; Zhang, Chengjian

doi:10.1007/s10092-018-0264-5

Cited by 15 publications

(2 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zhou and Stynes [14] constructed a class of BBVM for linear neutral Volterra integro-differential equations, Yan et al [15] extended the BBVM for solving numerically the nonlinear delay-differential-algebraic equations, Zhang and Yan [16] used the BBVM to find approximate solutions of nonlinear DDEs, and Zhao et al [35] applied the BBVM to the delay-differential-algebraic equation. A chronology of BBVMs can be seen in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions, Convergence and Global stability of delayed differential system with delay in the state variable of the Caputo derivative

Kumar,

Sharma,

Singh

2023

Preprint

View full text Add to dashboard Cite

The aim of this paper is to investigate the numerical solutions of delayed fractional differential equations (FDEs). A constant time delay is taken in the Caputo derivative of the state variable and also in the state variable. To obtain solutions, we extend the block boundary value method (BBVM) and show the convergence of the resulting scheme. Further, it is found that the order of convergence is $\min\{m,q-\delta+1\}$, where $m$ and $q$ are the order and block-size of the BBVM, respectively, and $\delta$ lies in between $0$ and $1$. In our methodology, we approximate the fractional-ordered derivative by a combination of the $m^{\text{th}}$-order BBVM and a $q^{\text{th}}$-order Lagrange interpolating polynomial. Lastly, we analyze the global stability of the numerical scheme and with the aid of some numerical examples, its computational effectiveness is proved. In examples, we analyse some fractional order delay differential systems and present a comparison of solutions for different fractional order derivatives. Furthermore, it is demonstrated that the global errors diminish as the order of the fractional derivative decreases, and this fact is supported by the theoretical order of convergence. MSC Classification: 34K37 , 34D23 , 65L20

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical solutions, Convergence and Global stability of delayed differential system with delay in the state variable of the Caputo derivative

Kumar,

Sharma,

Singh

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…For the temporal discretization, a good candidate is block boundary value methods (BBVMs) due to their excellent stability and high accuracy. For example, in References [14–16, 21–28], BBVMs were applied to ordinary differential equations (ODEs), differential‐algebraic equations, delay/functional differential equations and the temporal discretization of semi‐linear parabolic equations, space‐fractional diffusion equations and delay reaction–diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

Compact block boundary value methods for semi‐linear delay‐reaction–diffusion equations with algebraic constraints

Yan

Zhang

2020

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

In the present paper, we study a class of linear approximation methods for solving semi-linear delay-reaction-diffusion equations with algebraic constraint (SDEACs). By combining a fourth-order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated.

show abstract

Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments

Zhang

Yan

2020

Numer Algor

View full text Add to dashboard Cite

The adapted block boundary value methods for singular initial value problems

Cited by 15 publications

References 33 publications

Numerical solutions, Convergence and Global stability of delayed differential system with delay in the state variable of the Caputo derivative

Numerical solutions, Convergence and Global stability of delayed differential system with delay in the state variable of the Caputo derivative

Compact block boundary value methods for semi‐linear delay‐reaction–diffusion equations with algebraic constraints

Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments

Contact Info

Product

Resources

About