Abstract
This paper addresses the solution of one- and two-dimensional Volterra integral equations (VIEs) by means of the spectral collocation method. The novel technique takes advantage of the properties of shifted Jacobi polynomials and is applied for solving multi-dimensional VIEs. Several numerical examples demonstrate the efficiency of the method and an error analysis verifies the correctness and feasibility of the proposed method when solving VIE.
Conflict of interest: The authors declare that they have no conflict of interest.
References
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation
- Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn–Hilliard Equation
- On the Mittag–Leffler Stability of Impulsive Fractional Solow-Type Models
- Non-similarity Solutions for Viscous Dissipation and Soret Effects in Micropolar Fluid over a Truncated Cone with Convective Boundary Condition: Spectral Quasilinearization Approach
- Numerical Simulation of the Supersonic Disk-Gap-Band Parachute by Using Implicit Coupling Method
- Stochastic-Based RANS-LES Simulations of Swirling Turbulent Jet Flows
- Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections
- Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients
- Multiple-Wave Solutions to Generalized Bilinear Equations in Terms of Hyperbolic and Trigonometric Solutions
- Experimental and Simulation Analysis of the Successful Production of Heavy-Gauge Steel Plate by the Clad Rolling Process
- Jacobi Collocation Approximation for Solving Multi-dimensional Volterra Integral Equations
- A Note on Hidden Transient Chaos in the Lorenz System
- Finite Time Blow-up in a Delayed Diffusive Population Model with Competitive Interference
Articles in the same Issue
- Frontmatter
- The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation
- Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn–Hilliard Equation
- On the Mittag–Leffler Stability of Impulsive Fractional Solow-Type Models
- Non-similarity Solutions for Viscous Dissipation and Soret Effects in Micropolar Fluid over a Truncated Cone with Convective Boundary Condition: Spectral Quasilinearization Approach
- Numerical Simulation of the Supersonic Disk-Gap-Band Parachute by Using Implicit Coupling Method
- Stochastic-Based RANS-LES Simulations of Swirling Turbulent Jet Flows
- Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections
- Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients
- Multiple-Wave Solutions to Generalized Bilinear Equations in Terms of Hyperbolic and Trigonometric Solutions
- Experimental and Simulation Analysis of the Successful Production of Heavy-Gauge Steel Plate by the Clad Rolling Process
- Jacobi Collocation Approximation for Solving Multi-dimensional Volterra Integral Equations
- A Note on Hidden Transient Chaos in the Lorenz System
- Finite Time Blow-up in a Delayed Diffusive Population Model with Competitive Interference