Abstract
In this paper, we develop two-step collocation (2-SC) methods to solve two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the second kind. Here we convert a 2D-NVIE of the second kind to a one-dimensional case, and then we solve the resulting equation numerically by two-step collocation methods. We also study the convergence and stability analysis of the method. At the end, the accuracy and efficiency of the method is verified by solving two test equations which are stiff. In examples, we use the well-known differential transform method to obtain starting values.
Acknowledgements
The authors would like to thank the anonymous referees for their valuable comments that helped the authors to improve the paper.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Two-step collocation methods for two-dimensional Volterra integral equations of the second kind
- Riesz basis of exponential family for a hyperbolic system
- 𝜎-ideals and outer measures on the real line
- Some fractional differential equations involving generalized hypergeometric functions
- Global existence of solutions to nonlinear Volterra integral equations
- Second-order characterization of convex functions and its applications
- On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions
- Refinements of the Hermite–Hadamard inequality for co-ordinated convex mappings
- Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality
- Some families of sublinear correspondences
- Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations
- A note on the regularity of weak solutions to the coupled 2D Allen–Cahn–Navier–Stokes system
Artikel in diesem Heft
- Frontmatter
- Two-step collocation methods for two-dimensional Volterra integral equations of the second kind
- Riesz basis of exponential family for a hyperbolic system
- 𝜎-ideals and outer measures on the real line
- Some fractional differential equations involving generalized hypergeometric functions
- Global existence of solutions to nonlinear Volterra integral equations
- Second-order characterization of convex functions and its applications
- On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions
- Refinements of the Hermite–Hadamard inequality for co-ordinated convex mappings
- Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality
- Some families of sublinear correspondences
- Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations
- A note on the regularity of weak solutions to the coupled 2D Allen–Cahn–Navier–Stokes system