List questions from initial-value-problems

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Numerical Solver Exercise

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Two questions about PDE (sum of solutions)

Published on 11 May 2026 - 2:12

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For $y'=f(t,y),y(t_0)=y_0$ consider method $y_{i+1}=y_i+h(αf_i+(1-α)f_{i-1})$ where $f_k=f(t_k,y_k),α\in \mathbb R$. Find order of accuracy of method.

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ODE with non standard initial condition

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Numerical solution of a 1st order PDE

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Riccati ODE $y'(t)=(t^2+1)*y^2+t^2-1$, $y(0)=1$

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Numerically solving an initial value problem on an unbounded domain

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Solve initial value problem $u^{'}(t)=\frac{2(u(t))^{2}}{3(t+1)^{2}}$, $\ u(1)=3$

Published on 17 Apr 2026 - 3:00

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Problem getting the coefficients of a non-homogeneous PDE using the Fourier method

Published on 10 May 2026 - 21:55

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finding a solution for this recurrence relation

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Find Laplace transform of $t-\pi$

Published on 09 Apr 2026 - 12:01

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Finding initial conditions of 1-D Wave Equation PDE

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One Boundary Condition and One Initial Condition of PDE

Published on 11 May 2026 - 6:37

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Solving O.D.E and Initial Values Problem using Laplace Transform

Published on 09 Apr 2026 - 8:03

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Solving Initial Value Problems

Numerical Solver Exercise

Two questions about PDE (sum of solutions)

For $y'=f(t,y),y(t_0)=y_0$ consider method $y_{i+1}=y_i+h(αf_i+(1-α)f_{i-1})$ where $f_k=f(t_k,y_k),α\in \mathbb R$. Find order of accuracy of method.

ODE with non standard initial condition

Numerical solution of a 1st order PDE

Riccati ODE $y'(t)=(t^2+1)*y^2+t^2-1$, $y(0)=1$

Numerically solving an initial value problem on an unbounded domain

Solve initial value problem $u^{'}(t)=\frac{2(u(t))^{2}}{3(t+1)^{2}}$, $\ u(1)=3$

Problem getting the coefficients of a non-homogeneous PDE using the Fourier method

finding a solution for this recurrence relation

Find Laplace transform of $t-\pi$

Finding initial conditions of 1-D Wave Equation PDE

One Boundary Condition and One Initial Condition of PDE

Solving O.D.E and Initial Values Problem using Laplace Transform

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