### Abstract

In papers [1-3], we have formulated the conditions of the conservation of the main characteristic properties of the continuous problem to the numerical schemes in the case of homogeneous boundary conditions. Such properties are the conservation of the nonnegativity and the concavity of the initial function, monotonicity in time (contractivity) and others. In this paper, we consider similar questions to the problem with nonhomogeneous boundary conditions. We analyse the behaviour of the numerical solution in the limit by the time variable on some fixed mesh. We also consider the condition of the preservation of the nonnegativity and convexity (concavity) of the initial function. Finally, we examine the condition of the conservation of the monotonicity in the space variable of the initial function to the numerical solution.

Original language | English |
---|---|

Pages (from-to) | 143-150 |

Number of pages | 8 |

Journal | Computers and Mathematics with Applications |

Volume | 31 |

Issue number | 4-5 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Heat equation
- Monotonicity
- Numerical solution
- Qualitative properties

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

**Qualitative properties of the numerical solution of linear parabolic problems with nonhomogeneous boundary conditions.** / Faragó, I.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 31, no. 4-5, pp. 143-150.

}

TY - JOUR

T1 - Qualitative properties of the numerical solution of linear parabolic problems with nonhomogeneous boundary conditions

AU - Faragó, I.

PY - 1996

Y1 - 1996

N2 - In papers [1-3], we have formulated the conditions of the conservation of the main characteristic properties of the continuous problem to the numerical schemes in the case of homogeneous boundary conditions. Such properties are the conservation of the nonnegativity and the concavity of the initial function, monotonicity in time (contractivity) and others. In this paper, we consider similar questions to the problem with nonhomogeneous boundary conditions. We analyse the behaviour of the numerical solution in the limit by the time variable on some fixed mesh. We also consider the condition of the preservation of the nonnegativity and convexity (concavity) of the initial function. Finally, we examine the condition of the conservation of the monotonicity in the space variable of the initial function to the numerical solution.

AB - In papers [1-3], we have formulated the conditions of the conservation of the main characteristic properties of the continuous problem to the numerical schemes in the case of homogeneous boundary conditions. Such properties are the conservation of the nonnegativity and the concavity of the initial function, monotonicity in time (contractivity) and others. In this paper, we consider similar questions to the problem with nonhomogeneous boundary conditions. We analyse the behaviour of the numerical solution in the limit by the time variable on some fixed mesh. We also consider the condition of the preservation of the nonnegativity and convexity (concavity) of the initial function. Finally, we examine the condition of the conservation of the monotonicity in the space variable of the initial function to the numerical solution.

KW - Heat equation

KW - Monotonicity

KW - Numerical solution

KW - Qualitative properties

UR - http://www.scopus.com/inward/record.url?scp=0000857331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000857331&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000857331

VL - 31

SP - 143

EP - 150

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 4-5

ER -