GATE CE 2023 Set 1 — Question 52
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0HardSingle-Step Methods (ODEs)Numerical Integration & ODEsEngineering Mathematics
Engineering Mathematics → Numerical Integration & ODEs → Single-Step Methods (ODEs)
Last updated
Question
The differential equation,is solved by employing a backward difference scheme within the finite difference framework. The value of at the time-step, for some , is . The corresponding time is s. Each time step is s long. Then, the value of is ________________(round off to three decimal places).
Correct answer
-0.152
Solution
The backward difference scheme for the given differential equation is:Given:
s
s
sSubstituting the values into the finite difference equation:Solving the quadratic equation for :Taking the positive root:The value of is:Rounding to three decimal places, we get .
s
s
sSubstituting the values into the finite difference equation:Solving the quadratic equation for :Taking the positive root:The value of is:Rounding to three decimal places, we get .
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.