The initial-value problem for first order partial differential-functional equations

1995 ◽  
Vol 67 (4) ◽  
pp. 301-313
Author(s):  
Danuta Jaruszewska-Walczak
Keyword(s):  
Initial Value Problem ◽  
Functional Equations ◽  
Initial Value ◽  
Partial Differential ◽  
First Order

ORDER AND CONVERGENCE OF THE ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING INITIAL VALUE PROBLEM

2021 ◽  
Vol 5 (2) ◽  
pp. 442-446
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Necessary And Sufficient

This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems

scholarly journals Theory of differential offset continuation

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 718-732 ◽  
Author(s):  
Sergey Fomel
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Frequency Domain ◽  
Initial Value Problem ◽  
Data Transformation ◽  
Initial Value ◽  
Partial Differential ◽  
Reflection Data ◽  
Zero Offset

I introduce a partial differential equation to describe the process of prestack reflection data transformation in the offset, midpoint, and time coordinates. The equation is proved theoretically to provide correct kinematics and amplitudes on the transformed constant‐offset sections. Solving an initial‐value problem with the proposed equation leads to integral and frequency‐domain offset continuation operators, which reduce to the known forms of dip moveout operators in the case of continuation to zero offset.

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